Question

An ideal double slit interference experiment is performed with light of wavelength 640 nm. A bright spot is observed at the center of the resulting pattern as expected. For the 2n dark spot away from the center, it is known that light passing through the more distant slit travels the closer slit.

a) 480 nm
b) 600 nm
c) 720 nm
d) 840 nm
e) 960 nm

Answer 1

In a double-slit interference experiment, the wavelength of the light passing through the more distant slit can be found using the equation for path difference. By substituting the given wavelength and solving, the correct answer is (a) 480 nm.

Step-by-step explanation:

In a double-slit interference experiment, when a bright spot is observed at the center, the dark spots are located at regular intervals on either side. The dark spots, also known as minima, occur when waves from the two slits interfere destructively. The condition given in the question suggests that light passing through the more distant slit travels a path difference of 2n times the wavelength more compared to the light passing through the closer slit. Therefore, the wavelength of the light passing through the more distant slit is 2n times the wavelength of the given light.

To find the wavelength of the distant slit, we can use the equation for path difference:

Path difference = (wavelength of distant slit) - (wavelength of given light)

Substituting the values, we have:

2n × (wavelength) = (wavelength of distant slit) - (wavelength of given light)

Substituting the given wavelength (640 nm) and solving for the wavelength of the distant slit (W):

480 nm, 600 nm, 720 nm, 840 nm, 960 nm

Therefore, the correct answer is (a) 480 nm.