Question

The critical angle between an equilateral prism and air is 45°. If the incident ray is perpendicular to the refracting surface as shown below, then

• A. After deviation, it will emerge from the BC refracting side
• B. It is totally reflected on the BC and emerges out perpendicularly from the AC side in air
• C. It is totally reflected from the BC and AC refracting sides and finally emerges out from the AB side
• D. It is totally reflected from all the three sides of prism and never emerges out

Answer 1

The correct option is B

It is totally reflected on the BC and emerges out perpendicularly from the AC side in air

Let ray incident on surface AB, perpendicularly, so in triangle EDB, angle D = ${90}^{\circ }$.

So, angle DEB = ${180}^{\circ }-{90}^{\circ }-{60}^{\circ }={30}^{\circ }$

Also, angle DEB + $\angle i$ = ${90}^{\circ }$
So, $i={60}^{\circ }$
On surface BC, the angle of incidence > critical angle
$\therefore$ It will face total internal reflection.
Hence, it will totally be reflected on the second surface and emerges out perpendicularly from the third surface.