Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Diffraction asks what oscillates, what travels, and which wave quantity is being measured.
Common stuck point:Students often know a formula related to diffraction but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.
Sense of Study hint:Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?
Worked Examples
Example 1
easy
Sound waves (λ=1 m) pass through a doorway 0.8 m wide. Do the sound waves diffract significantly? Explain why you can hear someone around a corner.
Answer
Yes, significant diffraction occurs because λ≥gap width
First step
1
Diffraction is most significant when the wavelength is comparable to or larger than the gap size.
Full solution
2
Here λ=1 m>0.8 m (gap width), so significant diffraction occurs.
3
The sound waves spread out as they pass through the doorway, which is why you can hear people in other rooms even without a direct line of sight.
Diffraction is the bending and spreading of waves around obstacles or through gaps. It is most noticeable when the opening or obstacle is similar in size to the wavelength of the wave.
Example 2
medium
Light of wavelength 600 nm passes through a single slit of width 0.1 mm. At what angle does the first minimum of the diffraction pattern occur?
Example 3
medium
Light of wavelength λ=500 nm passes through a single slit of width a=0.02 mm. Find the angle to the first diffraction minimum using sinθ=λ/a.
Example 4
medium
Red (λ=700 nm) and blue (λ=450 nm) light pass through the same slit. Which color shows the wider diffraction pattern, and by what ratio do the first-minimum angles compare for small angles?
Example 5
medium
A WiFi router emits at λ=0.12 m. Estimate the spreading angle when waves pass through a doorway of width a=0.9 m using sinθ≈λ/a.
Example 6
hard
Through a single slit of width a=0.04 mm with λ=500 nm, find the angle to the second minimum using asinθ=mλ with m=2.
Example 7
hard
A grating has 600 lines/mm. For green light λ=540 nm, what is the highest order m that produces a visible maximum (need sinθ≤1)?
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
medium
Visible light (λ≈500 nm) and radio waves (λ≈1 m) both encounter a building 10 m wide. Which wave diffracts more around the building? Why?
Example 2
hard
A diffraction grating has 500 lines/mm. Light of wavelength 650 nm passes through it. At what angle does the second-order maximum appear?
Example 3
easy
What is diffraction?
Example 4
easy
Do sound waves diffract, or only light?
Example 5
easy
To make a wave spread out more after a gap, should the gap be narrower or wider?
Example 6
easy
Diffraction is strongest when the gap size is comparable to what wave property?
Example 7
easy
Why can you hear someone talking around a corner but not see them?
Example 8
easy
Does diffraction occur with water waves passing through a harbor gap?
Example 9
easy
Compared to visible light, do longer-wavelength radio waves diffract more or less around buildings?
Example 10
easy
Diffraction changes a wave's direction of spread. Does it change the wave's frequency?
Example 11
medium
Two slits have the same width, but slit A is illuminated with red light and slit B with blue light. Which produces wider diffraction spreading?
Example 12
medium
A gap is 0.5 mm wide. Diffraction is most significant for waves whose wavelength is closest to what value?
Example 13
medium
If you double the slit width while keeping wavelength fixed, does the diffraction spreading increase or decrease?
Example 14
medium
A wave with wavelength 2 cm meets a gap. Will it diffract more through a 2 cm gap or a 20 cm gap?
Example 15
medium
Diffraction limits the smallest detail an optical instrument can resolve. To see finer detail, should you use a longer or shorter wavelength?
Example 16
medium
A radio antenna emits waves of wavelength 3 m. Will these diffract noticeably around a 2 m wide pole?
Example 17
medium
Light and sound both pass through a doorway. Which diffracts more on the other side, and why?
Example 18
medium
Diffraction and refraction both change a wave's path. Which one requires a change of medium?
Example 19
medium
Ocean waves of wavelength 5 m approach a harbor opening. Will they spread more through a 5 m gap or a 50 m gap?
Example 20
challenge
Two waves, both wavelength λ, pass through gaps of width λ and width 5λ. The spreading angle scales roughly as λ/width. By what factor is the first gap's spreading larger?
Example 21
challenge
Why does a smaller telescope aperture give a more diffraction-blurred image than a larger one (same wavelength)?
Example 22
challenge
A single slit of width a=0.1 mm is lit with light of wavelength 500 nm. Estimate the half-angle to the first diffraction minimum using sinθ=λ/a.
Example 23
easy
Fill in the blank: diffraction is most noticeable when the gap size is approximately equal to the wave's ______.
Example 24
easy
Name the wave phenomenon: a wave bends around the edge of an obstacle without changing medium.
Example 25
easy
A sound wave of wavelength 0.7 m enters a doorway 0.8 m wide. Will the diffraction be significant?
Example 26
easy
Bass (low-frequency, long-wavelength) sound diffracts more readily than treble around obstacles. True or false?
Example 27
medium
A single slit of width a=0.05 mm is illuminated by λ=600 nm light. Where (angle) is the first minimum?
Example 28
medium
A diffraction grating has 300 lines/mm. For λ=500 nm, at what angle is the first-order maximum? Use dsinθ=mλ.
Example 29
medium
A sound wave with f=440 Hz travels at v=340 m/s. Find its wavelength and decide whether it diffracts strongly through a 0.8 m wide doorway.
Example 30
medium
Through a single slit of width a, the first diffraction minimum is at angle θ1 such that sinθ1=λ/a. If you halve the slit width, what happens to θ1 (assume small angle)?
Example 31
medium
A telescope has aperture D=0.1 m, used at λ=550 nm. Its diffraction-limited angular resolution is roughly θ≈1.22λ/D. Find θ in radians.
Example 32
medium
Why do CDs and DVDs show rainbow colors when light reflects off them?
Example 33
hard
A double-slit setup has slit separation d=0.2 mm and screen L=2.0 m away. With λ=600 nm, find the fringe spacing Δy=λL/d.
Example 34
hard
Sound at λ=0.5 m diffracts around a building of width w=10 m. Estimate the angular spread θ≈λ/w in degrees.
Example 35
hard
Two stars are separated by angular distance θ=1×10−6 rad. Can a telescope of aperture D=0.5 m at λ=550 nm resolve them? Use θmin=1.22λ/D.
Example 36
hard
Sound diffracts more easily than visible light through everyday gaps. Give the dominant physical reason in one sentence.
Example 37
hard
A water wave of wavelength λ=2 m approaches a harbor entrance of width a=4 m. Estimate the half-angle of diffraction spreading using sinθ≈λ/a.
Example 38
challenge
An electron has de Broglie wavelength λ=0.1 nm. A single slit of width a=100 nm produces a diffraction pattern. Find the angle to the first minimum.
Example 39
challenge
A diffraction grating with d=2×10−6 m is illuminated with two wavelengths, λ1=500 nm and λ2=510 nm. Find the angular separation of their first-order maxima.