AP EAMCET · PHYSICS · Wave Optics

In a diffraction pattern due to a single slit of width $' a'$ , the first minimum is observed at an angle $30 °$ when light of wavelength $500 nm$ is incident on the slit. The first secondary maximum is observed at an angle of

A $\sin^{- 1} \frac{1}{2}$
B $\sin^{- 1} \frac{3}{4}$
C $\sin^{- 1} \frac{1}{4}$
D $\sin^{- 1} \frac{2}{3}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\sin^{- 1} \frac{3}{4}$

Step-by-step Solution

Detailed explanation

Given that for slit of width a the first minimum form at θ=30°, the wavelength of light is 500 nm Using Bragg's law of diffraction, nλ=asinθ, here n is the whole number and for the first minimum n=1 …

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle 30° when light of wavelength 500 nm is incident on the slit. The first secondary maximum is observed at an angle of

Step-by-step Solution

In a diffraction pattern due to a single slit of width $' a'$ , the first minimum is observed at an angle $30 °$ when light of wavelength $500 nm$ is incident on the slit. The first secondary maximum is observed at an angle of