A transparent thin film of uniform thickness and refractive index $n_{1} = 1.4$ is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index $n_{2} = 1.5$ , as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance $f_{1}$ from the film, while rays of light traversing from glass to air get focused at distance $f_{2}$ from the film, Then

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$| f_{1} | = 3 R$

$| f_{2} | = 1.4 R$

$| f_{1} | = 2.8 R$

$| f_{2} | = 2 R$

answer is A, C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Question Image

$C a s e - I; \frac{n_{1}}{V^{'}} - \frac{1}{\infty} = \frac{n_{1} - 1}{R} \dots . (i) \frac{1.4}{V^{'}} = \frac{1.4 - 1}{R} \Rightarrow \frac{1.4}{V^{'}} = \frac{0.4}{R} V^{'} = \frac{7 R}{2} \frac{n_{2}}{f_{1}} - \frac{n_{1}}{V^{'}} = \frac{n_{2} - n_{1}}{R} \dots (2) \frac{n_{2}}{f_{1}} = \frac{n_{1} - 1}{R} + \frac{n_{2} - n_{1}}{R} \frac{n_{2}}{f_{1}} = \frac{n_{1} - 1 + n_{2} - n_{1}}{R} = \frac{n_{2} - 1}{R} f_{1} = \frac{n_{2} R}{n_{2} - 1} = \frac{1.5 R}{1.5 - 1} = \frac{1.5 R}{0.5} f_{1} = 3 R$

$C a s e - i i : \frac{n_{1}}{V^{'}} - \frac{n_{2}}{\infty} = \frac{n_{1} - n_{2}}{- R} \frac{n_{1}}{V^{'}} = \frac{n_{2} - n_{1}}{R} \dots (1) \frac{1}{f_{2}} - \frac{n_{1}}{V^{'}} = \frac{1 - n_{1}}{- R} = \frac{n_{1} - 1}{R} \dots . (2) (1) + (2) : \frac{1}{f_{2}} = \frac{n_{1} - 1 + n_{2} - n_{1}}{R} = \frac{n_{2} - 1}{R} \Rightarrow f_{2} = 2 R f_{2} = \frac{R}{n_{2} - 1} = \frac{R}{0.5} = 2 R$

Watch 3-min video & get full concept clarity

hear from our champions

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET