Question

Light of wavelength $\lambda$ is incident on a slit of width d and distance between screen and slit is $D$. Then width of maxima and width of slit will be equal if $D$ is--

• A. $\frac{d^2}{\lambda }$
• B. $\frac{2d^2}{\lambda }$
• C. $\frac{2d}{\lambda }$
• D. $\frac{d^2}{2\lambda }$

Answer 1

The correct option is D $\frac{d^2}{2\lambda }$

Th position of first minimum above the central maxima,

$y=\frac{\lambda D}{d}$. . . . . . . ..(1)

So, the linear width of the central maxima will be

$2y=\frac{2\lambda D}{d}$

According to question,

$\frac{2\lambda D}{d}=d$

$D=\frac{d^2}{2\lambda }$

The correct option is D.