Manipal Entrance Test 2015 Physics Paper

Rays comes out only from CD, means rays after refraction from AB get totally internally reflected at AD. From the figure,
r1+r2=90
⇒r1=90−r2
(r1)max=90°−(r2)max and (r2)min=θC
(for total internal reflection at AD)
where, sin‌θC=

n2

n1

or θC=sin−1(

n2

n1

)
∴(r1)max=90°−θC
Now, applymg Snell’s law at face AB, we wet

n1

n2

=

sin‌αmax

sin(r1)max

=

sin‌αmax

sin(90−θC)

=

sin‌αmax

cos‌θC

sin‌αmax=

n1

n2

‌cos‌θC
∴αmax=sin−1[

n1

n2

‌cos‌θC]
=sin−1[

n1

n2

‌cos(sin−1(

n2

n1

))]