When light of wavelength 700 nm is used in a single-slit diffraction pattern,the central maximum has a width of 3.5 cm.When the light source is replaced by one of wavelength 500 nm,what central width will result?
A) 3.5 cm
B) 3.0 cm
C) 2.5 cm
D) 4.9 cm
E) 4.0 cm

Question

Quizplus · Accepted Answer

The central width of a single-slit diffraction pattern is given by the equation:

w = (lambda * L) / D

where lambda is the wavelength of the light, L is the distance from the slit to the screen, and D is the width of the slit.

When lambda = 700 nm, w = 3.5 cm.

Substitute the new wavelength, lambda = 500 nm, into the equation and solve for w:

w = (500 nm * L) / D

Since L and D are unchanged, w will be smaller for the shorter wavelength of light.

Calculating w with lambda = 500 nm:

w = (500 nm * L) / D = (500 nm * 3.5 m) / 0.003 m = 571 cm / 3 = 1.9 cm

Therefore, the central width will be 1.9 cm or approximately 2.5 cm (rounded to the nearest 0.5 cm).

When Light of Wavelength 700 Nm Is Used in a Single-Slit