Question

A thin glass prism has refractive index \(1.5\). The correct relation between the angle of minimum deviation \((δm)\) and angle of refraction \((r)\) is

• A. \(δm = \frac{r}{2}\)
• B. \(δm = 2r\)
• C. \(δm = r\)
• D. \(δm = \frac{3r}{2}\)

Hint:

For a thin prism the deviation is (mu - 1) A, and at minimum deviation r equals A over 2.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a thin prism, the deviation is \(\delta=(\mu-1)A\). At minimum deviation the ray passes symmetrically, so the angle of refraction inside each face is \(r=\dfrac A2\).

Step 2: Compute
\[ \delta_m=(1.5-1)A=0.5A=\frac A2 \]
\[ r=\frac A2 \]

Step 3: Compare
\[ \delta_m=r \]

Step 4: Check the options
\(\delta_m=\frac r2\) would need \(\mu=1.25\). \(\delta_m=2r\) would need \(\mu=2\). \(\frac{3r}{2}\) would need \(\mu=1.75\). Only \(\delta_m=r\) matches \(\mu=1.5\), option (C).

Final Answer:
With index 1.5 the deviation is A over 2, which equals the angle of refraction r, option (C). \[ \boxed{\delta_m=r} \]