Question

A ray of light from a monochromatic point source of light is incident at a point on the screen. If a thin mica film of thickness 't' and refractive index 'n' is introduced in its path, then the optical path

• A. is increased by (n+1) t.
• B. is increased by (n-1) t.
• C. is decreased by (n+1) t.
• D. is not affected.

Hint:

Optical path equals refractive index times geometric thickness, so compare the path with and without the film.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Optical path in a medium of refractive index \(\mu\) and thickness \(x\) is \(\mu x\).

Step 2: Without the film
The thickness \(t\) is filled with air, so the optical path is \(1\times t=t\).

Step 3: With the film
The same thickness is filled with mica of index \(n\), so the optical path is \(nt\).

Step 4: Calculation
Change in optical path \(=nt-t=(n-1)t\), which is positive since \(n\gt 1\).

Final Answer:
The optical path is increased by \((n-1)t\). \[ \boxed{\text{(B) }\text{is increased by }(n-1)t} \]