SATHEE: Optics Question 100

Optics Question 100

Question: A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length 30cm. However, when silvered on the convex side it behaves like a concave mirror of focal length 10 cm. Then the refractive index of its material will be

[BHU 1997; UPSEAT 1995]

Options:

A) 3.0

B) 2.0

C) 2.5

D) 1.5

Show Answer

Answer:

Correct Answer: D

Solution:

Here $\frac{1}{F} = \frac{2}{f} + \frac{1}{f_{m}}$ Plano-convex lens silvered on plane side has $f_{m} = \infty$ .

$∴$ $\frac{1}{F} = \frac{2}{f} + \frac{1}{\infty} \Rightarrow \frac{1}{30} = \frac{2}{f} \Rightarrow f = 60 c m$ Plano-convex lens silvered on convex side has $f_{m} = \frac{R}{2}$

$∴$ $\frac{1}{F} = \frac{2}{f} + \frac{2}{R} \Rightarrow \frac{1}{10} = \frac{2}{60} + \frac{2}{R} \Rightarrow R = 30 c m$ Now using $\frac{1}{f} = (μ - 1) (\frac{1}{R})$ , we get $μ = 1.5$

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Optics Question 100

Question: A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length 30cm. However, when silvered on the convex side it behaves like a concave mirror of focal length 10 cm. Then the refractive index of its material will be

Options:

Answer:

Solution:

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