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Question

Refractive index of the medium on the left and right side of the spherical surface are 1 and 1.5 respectively. For the arrangement of object and spherical refracting surface as shown in figure, the position of image will be


A
+20 cm
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B
+45 cm
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C
45 cm
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D
+30 cm
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Solution

The correct option is B +45 cm
Suppose the image of the object O forms at I. The ray diagram can be drawn as:


Given,
μ1=1
μ2=1.5
The direction of incident ray is taken positive as per sign convention.

For refraction at the spherical surface we can use,
R=+6 cm
u=20 cm

Let the image distance be v

Using relation between object and image distance for refraction at curved surfaces:

μ2vμ1u=μ2μ1R

1.5v1(20)=1.51+6

Or, 1.5v=112120

v=(12×202012)×1.5

v=2408×1.5=45 cm

The +ve sign of image distance represents that image is formed in the direction of incident light.
Why this question ?
It intends to test your understanding of application of sign convention.

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