Question

The thickness of a plate (refractive index \(\mu\)) which will produce a change in optical path equal to half the wavelength \(\lambda\) of the light passing through it normally, is

• A. \(\frac{\lambda }{4(\mu -1)}\)
• B. \(\frac{3\lambda }{4(\mu -1)}\)
• C. \(\frac{\lambda }{(\mu -1)}\)
• D. \(\frac{\lambda }{2(\mu -1)}\)

Hint:

A plate of thickness t and refractive index mu adds an extra optical path of (mu - 1)t, so set this equal to half the wavelength.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
A plate of thickness \(t\) and refractive index \(\mu\) changes the optical path of light passing through it by \(\Delta=(\mu-1)t\).

Step 2: Apply the condition
The change is required to be half a wavelength, so \((\mu-1)t=\dfrac{\lambda}{2}\).

Step 3: Calculation
\(t=\dfrac{\lambda}{2(\mu-1)}\).

Step 4: Compare the options
This matches option (D).

Final Answer:
The required thickness is lambda divided by twice the quantity (mu minus 1). \[ \boxed{\text{(D) }\dfrac{\lambda}{2(\mu-1)}} \]