Answer to Question #162532 in Optics for Nama glory

Question

Consider a wave passing through a single slit. What happens to the width of the central maximum of its diffraction pattern as the slit is made half as wide as the first?

A. It becomes one-fourth as wide.

B. It becomes one half as wide

C. Its width does not change

D. It becomes twice as wide.

Answer 1

The central maximum lies between the first-order minima defined by the relation 

$$sin\theta_{dark}=\dfrac{m\lambda}{a}=\dfrac{\lambda}{a}$$

Because the angle is small, 

So,

$$sin\theta_{dark}\approx tan\theta_{dark}=\dfrac{y_{dark}}{L}$$

 

So, the width of the central maximum is proportional to $\dfrac{L\lambda}{a}$ .

Thus, the central maximum becomes twice as wide if the slit width a becomes half as wide.

So, according to the question, D option is correct.