# Double slit interference – problems and solutions

1. Yellow light passes through two slits and an interference pattern is observed on a screen.

(1) The bright fringes will increase in width if the yellow light is replaced blue

(2) The bright fringes will increase in width if the distance between slits minimized

(3) The intensity of light decreases if it is far from the central fringe

(4) The intensity of light is constant if it is far from the central fringe

Which is the correct statement?

Solution

*The distance between slits is smaller than the distance between the slit and screen so that angle is very small. Then,*

**The equation of double-slit interference (constructive interference****)**

*d = **distance between slits**, y =**Distance between bright line and the central fringe**, l = **distance between screen and slit**, n = orde**r**, **λ = **wavelength*

**(1) ****T****he bright ****fringes ****will increase in width if the yellow light is replaced blue**

Based on the above equation, the number of bright lines (n) is inversely proportional to the wavelength (λ). If the wavelength decreases, the number of bright lines (n) increases. Yellow light has a larger wavelength (smaller frequency) than blue light. If the yellow light is changed blue, the wavelength decreases, so the number of bright lines (n) increases.

*This statement is correct.*

**(2) ****The bright fringes will increase in width if the distance between slits minimized**

Based on the above formula, the distance between slits (d) is directly proportional to the number of bright lines (n). If the d istance between the slits is minimized, the number of bright lines (n) decreases.

*This statement is incorrect.*

**(3) **T**he intensity of light decreases if it is far from the cent****ral fringe**

Intensity relates to light level. Intensity is inversely proportional to the distance if the distance the greater the intensity the smaller (the light dimmer).

*This statement is correct.*

**(4) **The intensity of light is constant if it is far from the central fringe

*This statement is incorrect.*

2. A light falls on two slits 2-mm apart and produces on a screen 1 m away from the fourth-order bright line 1-mm from the center of the pattern. What is the wavelength of the light used?

__Known :__

Distance between slits (d) = 2 mm = 2 x 10^{-3 }m

Order (n) = 4

Distance between screen and slit (l) = 1 meter

Distance between the fourth-order bright line and the center of the pattern (y) = 1 mm = 1 x 10^{-3 }m = 10^{-3 }m

__Wanted :__ Wavelength (λ)

__Solution :__

The equation of the double slit interference :

d sin θ = n λ

The wavelength of the light (λ) :

3. Two slits 3-mm apart, 1 meter from the screen. If produced the sixth-order bright line 1-mm from the center of the pattern, what is the wavelength of the light used?

__Known :__

Distance between slits (d) = 3 mm = 3 x 10^{-3 }m

Order (n) = 6

Distance between screen and slit (l) = 1 meter

Distance between the sixth-order bright line and the center of the pattern (y) = 1 mm = 1 x 10^{-3 }m = 10^{-3 }meter

__Wanted :__ The wavelength of the light (λ)

__Solution :__

The wavelength of the light (λ)