Wave phenomena practice questions.

A ray of light in air strikes the surface of a transparent block at an angle of incidence of 45°. The angle of refraction inside the block is 30°. Determine the refractive index of the block.

• 0.71
• 0.87
• 1.4
• 1.5

Answer: 1.4

n = sin 45°/sin 30° = 0.707/0.500 = 1.4. Inverting the ratio gives 0.71 — a classic Snell's law error.

Monochromatic light passes obliquely from air into water. Which property of the light remains unchanged?

• Frequency
• Wavelength
• Speed
• Direction of travel

Answer: Frequency

The frequency is set by the source and does not change at a boundary. Speed and wavelength both decrease in water (v = fλ), and at oblique incidence the ray bends towards the normal.

Two coherent point sources emit waves of wavelength λ in phase. At point P the path difference between the waves from the two sources is 1.5λ. What is observed at P?

• Constructive interference
• Destructive interference
• No interference, because the waves are not coherent at P
• A displacement equal to the sum of the two amplitudes

Answer: Destructive interference

A path difference of (n + ½)λ means the waves arrive in antiphase, so they cancel — destructive interference. Constructive interference requires a whole-number multiple of λ.

Red light and blue light pass in turn through the same narrow slit, a few times wider than each wavelength. Which light diffracts through the larger angle, and why?

• the red light, because its wavelength is longer
• the blue light, because its frequency is higher
• the blue light, because it carries more energy
• both diffract equally, because the slit is unchanged

Answer: the red light, because its wavelength is longer

The amount of diffraction depends on the ratio of wavelength to gap width: the longer the wavelength relative to the slit, the greater the spreading, so red light diffracts more than blue. Reasoning from frequency or photon energy points the wrong way — diffraction is governed by wavelength alone.

A ray of light travels from water (n = 1.33) into glass (n = 1.52), meeting the boundary at an angle of incidence of 40°. Which statement describes the refracted ray?

• it bends away from the normal, because glass is denser
• it does not bend, because both media are transparent
• it is totally internally reflected at the boundary
• it bends towards the normal, because light slows in glass

Answer: it bends towards the normal, because light slows in glass

Light entering a medium of higher refractive index slows down and bends towards the normal — the rule holds between any two media, not just from air. Total internal reflection is impossible here because it requires travel from higher to lower refractive index.

A student writes: “Light inside glass of refractive index 1.5 meets the boundary with air at an angle of incidence of 60°. Since n₁ sin θ₁ = n₂ sin θ₂, sin θ₂ = 1.5 × sin 60° = 1.30, so θ₂ = 79°.” Identify the error.

• A sine can never exceed 1: the angle is past the critical angle of about 42°, so the light is totally internally reflected.
• The two refractive indices have been interchanged, so the ray actually leaves the glass at about 35° to the normal.
• Angles in the refraction equation are measured from the surface, so sin 30° should have been used in place of sin 60°.
• The arithmetic is correct, but the emerging ray bends towards the normal rather than away from it as it leaves.

Answer: A sine can never exceed 1: the angle is past the critical angle of about 42°, so the light is totally internally reflected.

An impossible sine is not an arithmetic slip but the physics telling you that no refracted ray exists. The critical angle here is arcsin(1/1.5) ≈ 42°, and 60° is beyond it, so all the light is reflected back into the glass.