Question

A ray of light travels from air to water to glass and again from glass to air. Refractive index of water with respect to air is 'x', glass with respect to water is 'y' and air with respect to glass is 'z'. Which one of the following is correct?

• A. \(xy = z\)
• B. \(xyz = 1\)
• C. \(xz = y\)
• D. \(yz = x\)

Hint:

Multiply the ratios n_w/n_a, n_g/n_w, n_a/n_g.

Answer 1

The Correct Option is B

Step 1: Test with numbers:
Take $n_a=1$, $n_w=\frac43$, $n_g=\frac32$. Then $x=\frac43$, $y=\frac{3/2}{4/3}=\frac98$, $z=\frac23$.

Step 2: Check:
$xyz=\frac43\cdot\frac98\cdot\frac23=\frac{72}{72}=1$. And $xy=\frac32\ne z$, $xz=\frac89\ne y$, $yz=\frac34\ne x$.

Step 3: Option:
(B).

Final Answer:
Test values confirm only xyz = 1. \[ \boxed{B} \]