CBSE Class 10 Science 2020 · Paper 31/2/3 · Question 29(b)

Light - Reflection and Refraction 5 marks Medium

(a)Define power of a lens and write its SI unit. Name the type of lens whose power is negative.
(b)A convex lens forms a real and inverted image of finite size at a distance of $50$ cm from it. Where is the object placed in front of the lens ? Give all possible positions of the object stating reason in each case.
(c)Draw labelled ray diagram for any one position of the object mentioned in (b) above.

Answer

Power is the reciprocal of focal length (dioptre); the object can be beyond $2 F_{1}$ , at $2 F_{1}$ or between $F_{1}$ and $2 F_{1}$ .

(a) The power of a lens is its ability to converge or diverge the rays of light falling on it; it is the reciprocal of its focal length,

P = \frac{1}{f}

(

f

in metres). Its SI unit is the dioptre (D),

1 D = 1 m^{- 1}

. A concave (diverging) lens has negative power. (b) A convex lens forms a real, inverted image of finite size only when the object is beyond

F_{1}

but not at infinity (between

O

and

F_{1}

the image is virtual and erect, at

F_{1}

it is at infinity, and for an object at infinity it is a point at

F_{2}

). The focal length is not given, so there are three possible positions: (i) Beyond

2 F_{1}

: the image lies between

F_{2}

and

2 F_{2}

and is diminished; this happens when

f

is between

25

cm and

50

cm. (ii) At

2 F_{1}

: the image is at

2 F_{2}

and of the same size; this happens when

f = 25

cm, the object being

50

cm from the lens. (iii) Between

F_{1}

and

2 F_{1}

: the image lies beyond

2 F_{2}

and is enlarged; this happens when

f

is less than

25

cm. (c) For the object at

2 F_{1}

with

f = 25

cm, the ray parallel to the axis refracts through

F_{2}

, the ray through

O

goes straight on, and the ray through

F_{1}

emerges parallel; they meet at

2 F_{2}

, giving a real, inverted image of the same size,

u = - 50

cm and

v = + 50

cm (see the labelled ray diagram).

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