# Worksheet: Double-Slit Diffraction

In this worksheet, we will practice calculating the characteristics of an interference pattern made by the diffraction of visible light through two slits.

Q1:

A double slit produces a diffraction pattern that is a combination of single- and double-slit interference, where the first minimum of the single-slit pattern falls on the fifth maximum of the double-slit pattern. Find the ratio of the width of the slits to the distance between the slits.

• A0.707 : 1
• B0.250 : 1
• C0.500 : 1
• D1.00 : 1
• E0.200 : 1

Q2:

When monochromatic light of wavelength 430 nm is incident on a double slit of slit separation 5 μm, there are 11 interference fringes in its central maximum. How many interference fringes will be in the central maximum of light of wavelength 632.8 nm for the same double slit?

Q3:

White light falls on two narrow slits separated by 0.40 mm. The interference pattern is observed on a screen 3.0 m away. The light in the interference pattern includes red light of wavelength 400 nm, yellow light of wavelength 600 nm, and violet light of wavelength 700 nm.

What is the separation between the first maxima for the red light and the violet light?

What is the angular distance to the nearest point to the central maximum at which a maximum for the yellow light will coincide with a maximum for the violet light?

What orders of maxima of the yellow light and the violet light will coincide nearest the central maximum?

• AYellow order 2 and violet order 5
• BYellow order 2 and violet order 4
• CYellow order 2 and violet order 3
• DYellow order 3 and violet order 4
• EYellow order 3 and violet order 5

Q4:

The first-order maximum for monochromatic light falling on a double slit is at an angle of .

At what angle is the second-order maximum?

What is the angle of the first minimum?

What is the highest-order maximum possible?

Q5:

Light of wavelength 720 nm is diffracted and the diffraction pattern produces a second-order maximum. What is the smallest separation between two slits that can produce this pattern?

Q6:

Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of .

Q7:

If both 500 nm light and 650 nm light each pass through two slits that are separated by 0.50 mm, how far apart are the second-order maxima for these two wavelengths on a screen 2.0 m away?

Q8:

600 nm wavelength light diffracts through two slits separated by 0.12 mm.

What is the angular position of the first maximum?

What is the angular position of the third maximum?

Q9:

Two slits are separated by a distance exactly five times the width of the slits. How many interference fringes lie in the central peak of the diffraction pattern?

Q10:

A monochromatic light of wavelength 590 nm is incident on two slits with a width of 3.2 μm each. A diffraction pattern is produced containing nine interference peaks inside the diffraction pattern central maximum. Find the separation of the slits.

Q11:

Young’s double-slit experiment is performed under water of refractive index 1.33. The light source is a He-Ne laser of in a vacuum.

What is the wavelength of this light in water?

What is the angle for the fifth-order maximum for two slits separated by 0.32 mm?

Q12:

The central diffraction peak of a double-slit interference pattern contains exactly seven peaks. What is the ratio of the slit separation to the slit width?

Q13:

Two slits of width 5.0 μm, each in an opaque material, are separated by a center-to-center distance of 6.0 μm. A monochromatic light of wavelength 690 nm is incident on the slits. A pattern is produced on the screen of bright and dark fringes, and within each bright fringe, a pattern of narrower bright and dark fringes is produced. How many maxima are produced within the central maximum of the larger-scale pattern?

Q14:

Two slits of width 3 μm, each in an opaque material, are separated by a center-to-center distance of 7 μm. A monochromatic light of wavelength 450 nm is incident on the double slit. A pattern of bright and dark fringes is produced on the screen, and within each bright fringe, a pattern of narrower bright and dark fringes is produced.

How many intensity maxima are produced within the central intensity maximum of the larger-scale pattern?

How many intensity maxima are produced within the central intensity maximum of the larger-scale pattern if the slit width is doubled while keeping the distance between the slits the same?

How many intensity maxima are produced within the intensity central maximum of the larger-scale pattern if the slit separation is doubled while keeping the slit width the same?