Question

In a double-slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0 cm. What happens to the distance between adjacent maxima when the slit separation is cut in half? 13) ______ A) It decreases to 0.25 cm. B) It decreases to 0.50 cm. C) It increases to 2.0 cm. D) It increases to 4.0 cm. E) None of these choices are correct.

Answer 1

Answer:

C) It increases to 2.0 cm

Explanation:

In a double-slit diffraction experiment, the distance on the screen between two adjacent maxima is given by

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

where

$\lambda$ is the wavelength of the wave

D is the distance of the screen from the slits

d is the separation between the slits

In this problem, the initial distance between adjacent maxima is 1.0 cm. Later, the slit separation is cut in a half, which means that the new slit separation is

$d'=\frac{d}{2}$

Substituting into the equation, we find that the new separation between the maxima is

$\Delta y' = \frac{\lambda D}{d/2}=2(\frac{\lambda D}{d})=2\Delta y$

So, the distance increases by a factor 2: therefore, the new separation between the maxima will be 2.0 cm.