CBSE Class 10 Science 2017 · Paper 31/2/1 · Question 22

Light - Reflection and Refraction 5 marks Medium

Analyse the following observation table showing variation of image-distance (

v

) with object-distance (

u

) in case of a convex lens and answer the questions that follow without doing any calculations :

(a)What is the focal length of the convex lens ? State reason for your answer.
(b)For what object-distance ( $u$ ) is the corresponding image-distance ( $v$ ) not correct ? How did you arrive at this conclusion ?
(c)Choose an appropriate scale to draw a ray diagram for the observation at S. No. 4 and find the approximate value of magnification.

S. No.	Object-Distance $u$ (cm)	Image-Distance $v$ (cm)
1	$- 60$	$+ 12$
2	$- 30$	$+ 15$
3	$- 20$	$+ 20$
4	$- 15$	$+ 30$
5	$- 12$	$+ 60$
6	$- 9$	$+ 90$

Answer

$f = + 10$ cm; the image distance for $u = - 9$ cm is wrong; the magnification for S. No. 4 is about $- 2$ .

(a) The focal length is

10

cm (

f = + 10

cm). Reason: at S. No. 3 the object and the image are both 20 cm from the lens. A convex lens forms a real image as far from the lens as the object only when the object is at

2 F_{1}

(the image then forms at

2 F_{2}

), so

2 f = 20

cm and

f = 10

cm. (b) The image distance is not correct for

u = - 9

cm (S. No. 6). With

f = 10

cm, an object 9 cm from the lens lies between the optical centre and

F_{1}

. A convex lens then forms a virtual, erect, magnified image on the same side as the object, so

v

must be negative; a real image at

v = + 90

cm is not possible. (c) With a scale of 1 cm to 5 cm the object is drawn 3 cm from the lens, the foci 2 cm from it, and the rays meet 6 cm (30 cm to scale) beyond the lens. The image is real, inverted and about twice as tall as the object, so the magnification is approximately

- 2

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CBSE Class 10 Science 2017 · Paper 31/2/1 · Question 22

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