A plano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 60 cm. However, when silvered on the convex side, it behaves like a concave mirror of focal length 20 cm. Then, the refractive index of the lens is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

2.0

1.5

1.0

3.0

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{1}} + \frac{1}{f_{m}}$
$\Rightarrow$ $\frac{1}{F} = \frac{2}{f_{1}} + \frac{1}{f_{m}}$ $\Rightarrow$ $\Rightarrow$ $\frac{1}{F} = 2 (μ - 1) (\frac{1}{R}) + \frac{1}{\infty}$ $\Rightarrow$ $F = \frac{R}{2 μ (- 1)}$ $\Rightarrow$ $- 60 = \frac{- R}{2 (μ - 1)}$ $\Rightarrow$ $120 (μ - 1) = R$
$\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{1}} + \frac{1}{f_{m}}$ $\Rightarrow$ $\frac{1}{F} = \frac{2}{f_{1}} + \frac{1}{R / 2}$ $\Rightarrow$ $\frac{1}{F} 2 (μ - 1) (\frac{1}{R}) + \frac{2}{R}$ $\Rightarrow$ $\frac{1}{F} = \frac{2}{F} (μ - 1 + 1)$ $\Rightarrow$ $F = \frac{R}{2 μ}$ $\Rightarrow$ $- 20 = \frac{- R}{2 g μ}$ $\Rightarrow$ $40 μ = R$
Dividing (1) and (2) , we get
$\frac{120 (μ - 1)}{40 μ} = \frac{R}{R} = 1$ $\Rightarrow$ $120 (μ - 1) = 40 μ$ $\Rightarrow$ $120 μ - 40 μ = 120$ $\Rightarrow$ $80 μ = 120$