SATHEE: Optics Question 126

Optics Question 126

Question: There is an equiconvex glass lens with radius of each face as R and $_{a} μ_{g} = 3 / 2$ and $_{a} μ_{w} = 4 / 3$ . If there is water in object space and air in image space, then the focal length is

Options:

A) 2R

B) R

C) 3 R/2

D) $R^{2}$

Show Answer

Answer:

Correct Answer: C

Solution:

Consider the refraction of the first surface i.e. refraction from rarer medium to denser medium

$\frac{μ_{2} - μ_{1}}{R} = \frac{μ_{1}}{- u} + \frac{μ_{2}}{v_{1}}$

$\Rightarrow$ $\frac{(\frac{3}{2}) - (\frac{4}{3})}{R} = \frac{\frac{4}{3}}{\infty} + \frac{\frac{3}{2}}{v_{1}} \Rightarrow v_{1} = 9 R$

Now consider the refraction at the second surface of the lens i.e. refraction from denser medium to rarer medium $\frac{1 - \frac{3}{2}}{- R} = - \frac{\frac{3}{2}}{9 R} + \frac{1}{v_{2}} \Rightarrow v_{2} = (\frac{3}{2}) R$

The image will be formed at a distance of $\frac{3}{2} R$ .

This is equal to the focal length of the lens.

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Optics Question 126

Question: There is an equiconvex glass lens with radius of each face as R and aμg=3/2 and aμw=4/3 . If there is water in object space and air in image space, then the focal length is

Options:

Answer:

Solution:

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Question: There is an equiconvex glass lens with radius of each face as R and $_{a} μ_{g} = 3 / 2$ and $_{a} μ_{w} = 4 / 3$ . If there is water in object space and air in image space, then the focal length is