Class 10 Science · Chapter 9

Light - Reflection and Refraction

409 Class 10 Science questions on Light - Reflection and Refraction from the NCERT textbook, NCERT Exemplar and CBSE board papers 2017–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Science previous year papers, with answers →

Questions · page 18 of 21

1. Q341 CBSE 2017
   List ​four ​characteristics ​of ​the ​images formed ​by plane ​mirrors.
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   The image is virtual, erect, the same size as the object, and as far behind the mirror as the object is in front.

   Any four of the following. The image formed by a plane mirror is: (i) Virtual — it cannot be obtained on a screen. (ii) Erect (upright). (iii) Of the same size as the object. (iv) As far behind the mirror as the object is in front of it. (v) Laterally inverted — the left side of the object appears as the right side of the image.

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2. Q342 CBSE 2017
   State ​two laws of ​reflection ​of ​light.
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   The angle of incidence equals the angle of reflection, and the incident ray, normal and reflected ray lie in one plane.

   Law 1: The angle of incidence is equal to the angle of reflection, $\angle i=\angle r$, both measured from the normal at the point of incidence. Law 2: The incident ray, the normal to the mirror at the point of incidence and the reflected ray all lie in the same plane.

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3. Q343 CBSE 2017
   Draw a ray diagram to ​show ​the formation of real image of an object when ​refraction of light takes place through a convex lens. Mark as per ​the new Cartesian sign ​convention the object-distance ($u$), image distance ($v$) and the focal length ($f$) and ​also write ​the relation between $u$, $v$ and $f$.
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   Object beyond $2F_1$ gives a real, inverted image between $F_2$ and $2F_2$; $u$ is negative, $v$ and $f$ positive; $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$.

   Ray diagram (drawn to scale for an object $30$ cm from a convex lens of focal length $10$ cm): the object $AB$ stands on the principal axis beyond $2F_1$. A ray from $A$ parallel to the principal axis passes through $F_2$ after refraction, and a ray from $A$ through the optical centre $O$ goes straight on. They meet at $A^{\prime }$ below the axis, so the image $A^{\prime }{B}^{\prime }$ is real and inverted (here diminished, between $F_2$ and $2F_2$). Sign convention: all distances are measured from $O$; those in the direction of the incident light (to the right of the lens) are positive and those against it (to the left) are negative. So the object distance $u=OB$ is negative, the image distance $v=O{B}^{\prime }$ is positive and the focal length $f=O{F}_2$ of the convex lens is positive — in the figure $u=-30$ cm, $v=+15$ cm and $f=+10$ cm. Relation between $u$, $v$ and $f$ (lens formula): $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$.

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4. Q344 CBSE 2017
   An object ​is placed perpendicular to ​the principal axis of ​a convex lens of focal length 8 cm. The distance ​of the object ​from the lens is 12 cm. Find the position and ​nature ​of the image.
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   $v=+24$ cm: a real, inverted image, twice the size of the object, on the other side of the lens.

   Position: $v=+24$ cm. The image is formed $24$ cm from the lens, on the other side of the lens from the object (beyond $2F_2$). Nature: real and inverted. It is also magnified, twice the size of the object, since $m=\frac{v}{u}=\frac{+24}{-12}=-2$.

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5. Q345 CBSE 2017
   State ​Snell’s law of refraction of light. Express it mathematically. Write ​the relationship ​between absolute refractive index of a ​medium ​and speed of light in vacuum.
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   The ratio $\frac{\sin i}{\sin r}$ is constant for a given pair of media; absolute refractive index is $n=\frac{c}{v}$.

   Snell’s law: the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for light of a given colour and for a given pair of media. Mathematically: $\frac{\sin i}{\sin r}=\text{constant}=n_{21}$, the refractive index of the second medium with respect to the first. Absolute refractive index: $n_m=\frac{c}{v}$, where $c$ is the speed of light in vacuum ($3\times 10^8$ m/s) and $v$ is the speed of light in the medium.

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6. Q346 CBSE 2017
   Define the ​term magnification as referred to spherical mirrors. If a concave mirror forms a real image 40 cm from the mirror, ​when the ​object is placed ​at a distance ​of 20 ​cm from its ​pole, find the focal length of the ​mirror.
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   Magnification is the ratio of image height to object height; the focal length is $-\frac{40}{3}$ cm, about $-13.3$ cm.

   Magnification: the magnification produced by a spherical mirror is the ratio of the height of the image ($h^{\prime }$) to the height of the object ($h$), $m=\frac{h^{\prime }}{h}=-\frac{v}{u}$. It tells how many times the image is magnified compared with the object. Focal length: $u=-20$ cm and, since the real image is formed in front of the mirror, $v=-40$ cm. Then $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=-\frac{1}{40}-\frac{1}{20}=-\frac{3}{40}$, so $f=-\frac{40}{3}$ cm $\approx -13.3$ cm. The focal length of the concave mirror is about $13.3$ cm (negative by the sign convention).

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7. Q347 CBSE 2017
   Draw each of the following diagrams ​on ​your ​answer ​sheet and show ​the ​path ​of ray after ​reflection.

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   The ray at the pole reflects with $\angle r=\angle i$; rays towards or through $F$ reflect parallel to the principal axis.

   (i) The mirror is convex and the ray strikes its pole $P$, where the normal is the principal axis. The reflected ray goes back below the principal axis, making the same angle with the axis as the incident ray: $\angle r=\angle i$. (ii) The mirror is convex and the ray is directed towards its principal focus $F$, which lies behind the mirror. After reflection the ray travels parallel to the principal axis, back towards the side it came from. (iii) The mirror is concave and the ray passes through its principal focus $F$. After reflection the ray travels parallel to the principal axis, back towards the side it came from, below the axis.

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8. Q348 CBSE 2017
   Draw each of the ​following diagrams on your answer-sheet and show the ​path of ​the ray ​after ​reflection in ​each case.

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   The ray at the pole reflects with $\angle r=\angle i$; rays towards or through F reflect parallel to the principal axis.

   (i) The ray strikes the convex mirror at its pole P, where the normal is the principal axis. It is reflected on the other side of the principal axis, making an equal angle with it ($\angle i=\angle r$). (ii) The ray is directed towards the principal focus F of the convex mirror, so after reflection it travels parallel to the principal axis. (iii) The ray passes through the principal focus F of the concave mirror, so after reflection it travels parallel to the principal axis. The completed diagrams are shown in the figure.

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9. Q349 CBSE 2017
   A student wants to focus the image of a candle flame placed at ​a distance of 80 cm ​from the optical centre of a lens ​on a ​screen placed at a distance of 20 ​cm from its optical centre.

   1. (a)What type of lens should he use ​? Answer stating reason.
   2. (b)Find (i) the distance between the object and its image and (ii) the magnification of the image. (c) ​Draw a ray diagram to show the formation of ​image in this case.
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   A convex lens; the object and image are 100 cm apart; $m=-0.25$ (real, inverted, one-fourth size).

   (a) A convex (converging) lens. The image is obtained on a screen, so it is real, and of the two kinds of lens only a convex lens can form a real image of a real object; a concave lens always forms a virtual image. The lens formula agrees: $\frac{1}{f}=\frac{1}{20}-\frac{1}{-80}=\frac{5}{80}$, so $f=+16$ cm, which is positive. (b) (i) The flame and the screen are on opposite sides of the lens, so the distance between the object and its image is $80+20=100$ cm. (ii) $m=\frac{v}{u}=\frac{+20}{-80}=-0.25$: the image is real, inverted and one-fourth the size of the flame. (c) The flame is beyond $2F_1$. A ray from its tip parallel to the axis passes through $F_2$ after refraction, and a ray through the optical centre goes on undeviated; they meet $20$ cm behind the lens, between $F_2$ and $2F_2$, where the screen is (see the ray diagram).

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10. Q350 CBSE 2017
    Draw each ​of ​the following diagrams ​on your answer sheet ​and ​show the ​path of ​the ray after ​refraction.

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    Convex lens: parallel ray passes through $F_2$, ray through $F_1$ emerges parallel; concave lens: parallel ray appears to come from $F_1$.

    (i) The ray, parallel to the principal axis, falls on a convex lens. After refraction it bends towards the axis and passes through the principal focus F on the other side of the lens ($F_2$). (ii) The ray passes through the principal focus F on the side of the incident light ($F_1$) and falls on a convex lens. After refraction it emerges parallel to the principal axis. (iii) The ray, parallel to the principal axis, falls on a concave lens. After refraction it bends away from the axis, so that it appears to diverge from the principal focus F on the same side as the incident light ($F_1$); this backward extension is drawn dashed. (The three completed ray diagrams are shown.)

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11. Q351 CBSE 2017
    An ​object is ​placed ​perpendicular to the principal axis of a convex ​lens of focal length 18 cm. The distance of ​the object from the lens ​is ​27 cm. Find the position and nature of the image formed.
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    $v=+54$ cm: a real, inverted image, twice the size of the object, formed on the other side of the lens, beyond $2F_2$.

    Position: $v=+54$ cm. The image is formed $54$ cm from the lens, on the other side of the lens from the object (beyond $2F_2$, since $2f=36$ cm). Nature: real and inverted, and magnified to twice the size of the object, since $m=\frac{v}{u}=\frac{+54}{-27}=-2$.

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12. Q352 CBSE 2017
    A child ​has a spherical mirror of focal length ​15 cm and he observes ​an erect and magnified image of his face in the mirror. State the type of mirror used by him and nature of the ​image he ​observes. What should ​be the range of ​distance of the mirror from his face ? Draw ray diagram to justify your answer.
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    A concave mirror; the image is virtual, erect and magnified; the face must be less than 15 cm from the mirror.

    Type of mirror: a concave mirror. Nature of the image: virtual, erect and magnified (enlarged), formed behind the mirror. Range of distance: the face must be between the pole and the principal focus of the mirror, that is, at a distance of less than 15 cm from the mirror. Ray diagram: with the face AB between P and F, a ray from A parallel to the principal axis is reflected through F, and a ray along the line from C is reflected back along itself. The reflected rays diverge; their backward extensions meet behind the mirror at A′, giving a virtual, erect, enlarged image A′B′. For example, with the face 10 cm away, $v=+30$ cm and $m=+3$.

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13. Q353 CBSE 2017
    An object $4$ cm ​in height, is placed at $15$ cm in front of ​a concave mirror ​of focal length $10$ cm. At what distance from the mirror should a ​screen be ​placed to obtain a sharp image of ​the object. Calculate the ​height of the image.
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    The screen is placed 30 cm in front of the mirror; the image is real, inverted and 8 cm tall.

    The screen should be placed $30$ cm in front of the mirror, on the same side as the object ($v=-30$ cm). The height of the image is $8$ cm ($h^{\prime }=-8$ cm); the minus sign shows that the image is inverted. The image is real and magnified, twice the height of the object ($m=-2$).

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14. Q354 CBSE 2017
    A 3 cm tall object ​is placed 18 cm in front of a concave mirror of focal length 12 cm. At what distance from the ​mirror ​should a screen be placed to see a sharp image ​of ​the object on the screen. Also ​calculate the height of the image formed.
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    The screen should be 36 cm in front of the mirror; the image is 6 cm tall (inverted, real, twice the size).

    The screen should be placed $36$ cm in front of the mirror, on the same side as the object ($v=-36$ cm). The height of the image is $6$ cm ($h^{\prime }=-6$ cm); the minus sign shows that the image is inverted. The image is real and magnified, twice the height of the object ($m=-2$).

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15. Q355 CBSE 2017
    The image of a candle flame ​placed at a distance of 30 cm from a mirror is ​formed on a screen placed in front of the mirror at a distance of 60 cm ​from its pole. What is the nature of ​the ​mirror ? Find its focal length. If the ​height of the flame is 2.4 cm, find the height of its image. State ​whether the image formed is erect or inverted.
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    Concave mirror; $f=-20$ cm; the image is 4.8 cm tall ($h^{\prime }=-4.8$ cm) and inverted.

    Nature of the mirror: concave, because the image is formed on a screen, so it is real, and only a concave mirror can form a real image of a real object. Focal length: with $u=-30$ cm and $v=-60$ cm, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=-\frac{1}{60}-\frac{1}{30}=-\frac{1}{20}$, so $f=-20$ cm (a focal length of 20 cm). Height of the image: $m=-\frac{v}{u}=-2$, so $h^{\prime }=m\times h=-2\times 2.4=-4.8$ cm; the image is 4.8 cm tall. The image is inverted (the negative sign of $m$ and $h^{\prime }$), as well as real and magnified.

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16. Q356 CBSE 2017
    The magnification ​of an image formed by a lens is $-1$. If the distance of the image ​from the optical centre of the lens is 25 cm, where is the object placed ​? Find the nature ​and focal ​length of the ​lens. If the object is displaced 15 cm towards the optical centre of the ​lens, where would the image be formed ? Draw a ray diagram to justify ​your answer.
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    Object at $u=-25$ cm ($2F_1$); convex lens, $f=+12.5$ cm; after shifting, $v^{\prime }=-50$ cm, a virtual, erect image five times as tall.

    The object is placed 25 cm from the optical centre on the other side of the lens from the image ($u=-25$ cm), that is at $2F_1$, and the image is at $2F_2$. The lens is converging (convex), with focal length $f=+12.5$ cm. When the object is moved 15 cm towards the optical centre it is 10 cm from the lens ($u=-10$ cm), inside the focal length. The image then forms 50 cm from the lens on the same side as the object ($v=-50$ cm); it is virtual, erect and five times as tall ($m=+5$). In the ray diagram the two emergent rays diverge and their backward extensions meet at that point.

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17. Q357 CBSE 2017
    The ​magnification of an image formed by ​a lens is $-1$. If ​the distance ​of the image from the ​optical centre of the lens is 35 cm, where is the object placed ​? What ​is the nature and focal length of the lens ? If the object is displaced 20 cm towards the ​optical centre of the lens, where would the image be formed and what will be its nature ? Draw a ray diagram to justify your answer.
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    Object at 35 cm from a convex lens, $f=+17.5$ cm; after moving 20 cm closer, a virtual, erect image forms 105 cm away.

    The object is placed 35 cm in front of the lens ($u=-35$ cm), on the other side from the image — that is, at $2F_1$, with the image at $2F_2$. The lens is convex (converging), with focal length $f=+17.5$ cm. When the object is moved 20 cm towards the optical centre it is 15 cm from the lens ($u=-15$ cm), inside the focal length. The image is then formed 105 cm from the lens on the same side as the object ($v=-105$ cm); it is virtual, erect and magnified 7 times ($m=+7$). The ray diagram shows the two emergent rays diverging, with their backward extensions meeting at the image.

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18. Q358 CBSE 2017
    The magnification of an image formed by a lens is $-1$. ​If the distance between the object and its image ​is 60 cm, what is ​the distance of the object from the ​optical centre of the lens ? Find the nature and focal length of the ​lens. If the object is displaced ​20 cm towards ​the optical centre of the lens, where would the image be formed and what would be its nature ? Draw a ray diagram to justify your answer.
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    Object at $u=-30$ cm; convex lens, $f=+15$ cm; after moving, $v^{\prime }=-30$ cm, a virtual, erect image three times the size.

    The object is 30 cm from the optical centre ($u=-30$ cm), with the image 30 cm from the lens on the other side ($v=+30$ cm); the object is at $2F_1$. The lens is a converging (convex) lens of focal length $f=+15$ cm. When the object is displaced 20 cm towards the optical centre, it is 10 cm from the lens ($u=-10$ cm), between $F_1$ and $O$. The image is then formed 30 cm from the lens on the same side as the object ($v=-30$ cm); it is virtual, erect and magnified, three times the size of the object ($m=+3$). In the ray diagram the two refracted rays diverge, and their backward extensions meet at that point.

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19. Q359 CBSE 2017
    If the image formed by a lens for all positions of ​an object placed in front of it is ​always erect and ​diminished, what is the nature of this lens ? Draw a ray ​diagram to justify your answer. If the numerical value of the ​power of this lens is 10 D, what is its focal length ​in the Cartesian ​system ?
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    Concave (diverging) lens; its image is always virtual, erect and diminished; $P=-10$ D gives $f=-10$ cm.

    The lens is a concave (diverging) lens: for every position of the object it forms a virtual, erect and diminished image between its focus $F_1$ and its optical centre, as the ray diagram shows. A concave lens has a negative power, so $P=-10$ D and $f=\frac{1}{P}=\frac{1}{-10}$ m $=-0.1$ m $=-10$ cm.

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20. Q360 CBSE 2017
    Draw ray ​diagrams to ​show the formation of three times magnified ​

    1. (a)real, ​and ​
    2. (b)​virtual image of an object by ​a converging lens. Mark the positions of O, F ​and 2F in each diagram.
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    Real image ($m=-3$): object between $F_1$ and $2F_1$; virtual image ($m=+3$): object between $O$ and $F_1$.

    (a) Real image, three times magnified ($m=-3$): place the object between $F_1$ and $2F_1$, at $u=-\frac{4f}{3}$. The ray parallel to the principal axis is refracted through $F_2$, and the ray through the optical centre $O$ goes straight on; they meet beyond $2F_2$, at $v=+4f$, forming a real, inverted image three times the height of the object (first ray diagram). (b) Virtual image, three times magnified ($m=+3$): place the object between $O$ and $F_1$, at $u=-\frac{2f}{3}$. The refracted rays diverge; their backward extensions meet on the object's side at $v=-2f$, the position of $2F_1$, forming a virtual, erect image three times the height of the object (second ray diagram). $O$, $F_1$, $F_2$, $2F_1$ and $2F_2$ are marked on the principal axis in both diagrams.

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