Question

In a single slit diffraction experiment, for wavelength '\(λ\)', half angular width of the principal maxima is '\(θ\)'. Also for wavelength of light '\(pλ\)', the half angular width of the principal maxima is '\(qθ\)'. The ratio of the half angular widths of the first secondary maxima in the first case to second case will be

• A. \(p:1\)
• B. \(1:q\)
• C. \(p:q\)
• D. \(q:p\)

Hint:

Half angular width of the principal maximum is \(\theta=\dfrac\lambda a\); the first secondary maximum lies near \(\dfrac{3\lambda}{2a}\).

Answer 1

The Correct Option is B

Step 1: Link the two angles
The secondary maximum angle is a fixed multiple, $\tfrac32$, of the central half-width for the same slit and wavelength.

Step 2: Take the ratio
The multiple cancels, leaving the ratio of half-widths, $\theta:q\theta=1:q$, option (B).

Final Answer:
The ratio is $1:q$, option (B). \[ \boxed{1:q} \]