1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In the figure shown below, find the minimum value of i for which total internal reflection never takes place at P. [Medium surrounding the slab has refractive index μ2]

A
cos1(1817)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
sin1(817)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
cos1(178)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
sin1(178)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D sin−1(√178)For no total internal reflection at P: β≤θc In critical case, β=θc So, r=90∘−β=90∘−θc....(1) We know , sinθc=μ2μ1 ⇒sinθc=4332=89 ............(2) Applying snell's law at point Q μ2sini=μ1sinr Substituting the given data we get, 43sini=32sin(90∘−θc) [ From (1) ] ⇒89sini=cosθc ⇒89sini=√1−sin2θc ⇒89sini=√1−6481 [ From (2) ] ⇒89sini=√179 ⇒sini =√178 ⇒i=sin−1(√178) Hence, option (d) is the correct answer. Why this question? This question check your ability to apply geometry and trigonometry in the Snell's law to get the required data. Such questions are generally asked in JEE Main.

Suggest Corrections
4
Join BYJU'S Learning Program
Related Videos
Apparent Depth
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program