Question

On a hypotenuse of a right prism (30^∘-60^∘-90^∘) of refractive index 1.50, a drop of liquid is placed as shown in figure. Light is allowed to fall normally on the short face of the prism. In order that the ray of light may get totally reflected, the maximum value of refractive index of the liquid is 

• A. 1.30
• B. 1.47
• C. 1.20
• D. 1.25

Hint:

For total internal reflection: n₂ ≤ n₁ sin i Maximum refractive index of the outer medium occurs when i = c.

Answer 1

The Correct Option is B

Step 1: Light enters the prism normally, so it travels undeviated inside.

Step 2: Angle of incidence at the hypotenuse: i = 60^∘ 

Step 3: For total internal reflection at prism–liquid interface: sin c = fracnlᵢqᵤᵢdnprism and i ≥ c 

Step 4: Maximum nlᵢqᵤᵢd occurs when i=c: nlᵢqᵤᵢd = nprism sin i = 1.5 × sin 60^∘ nlᵢqᵤᵢd = 1.5 × frac√(3)2 ≈ 1.47