Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

A ray of light AO in vacuum is incident on a glass slab at angle $60^{\circ}$ and

refracted at angle $30^{\circ}$ along OB as shown in the figure. The optical path length of light

ray from A to B is :

Option 1)
$\frac{2\sqrt3}{a}+2b$

Option 2)
$2a+\frac{2b}{3}$

Option 3)
$2a+\frac{2b}{\sqrt3}$

Option 4)
$2a+2b$

Answers (1)

best_answer

Optical Path -

$x{}'=\mu \cdot x$

- wherein

$x{}'=$ Distance travelled in vacuum

$x=$ Distance travelled in a medium of refractive index $\mu$

Optical path = AO + $\mu$ ( OB )

Apply Snells law ,

$1\cdot sin60^{\circ}=\mu \cdot sin30^{\circ}$

$\mu=\frac{\sqrt3}{2}/\frac{1}{2}=\sqrt3$

$sin 30^{\circ}=\frac{a}{AO}$

So, $AO = 2a$

Similarly,

$cos30^{\circ}=\frac{b}{OB}$

=> $OB=\frac{b}{cos30^{\circ}}$

=> $OB=\frac{2}{\sqrt3}b$

So, optical path = AO + $\mu$ ( OB )

= $2a+(\sqrt3\times \frac{2}{\sqrt3}b)$

= 2a+2b

Option 1)

$\frac{2\sqrt3}{a}+2b$

Option 2)

$2a+\frac{2b}{3}$

Option 3)

$2a+\frac{2b}{\sqrt3}$

Option 4)

$2a+2b$

Posted by

solutionqc

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

Engineering aspirant dies by suicide in Kota, fourth case this year

anam-khan

What is non-Aadhaar declaration in JEE Main 2025? Explain mismatch between image, face

anam-khan

Forgot JEE Main password 2025 for downloading admit card? Here’s what to do

Latest Question