Reflection Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Reflection.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The change in direction of a wave at a boundary so that it returns into the original medium.

Like a ball bouncing off a wall—the wave reverses direction at the boundary.

Read the full concept explanation →

How to Use These Examples

  • 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: Reflection asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to reflection 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
A light ray hits a plane mirror at an angle of 35°35° to the normal. What is the angle of reflection?

Answer

θr=35°\theta_r = 35°

First step

1
The given 35°35° is the angle of incidence because it is measured to the normal.

Full solution

  1. 2
    By the law of reflection, the angle of incidence equals the angle of reflection.
  2. 3
    θr=θi=35°\theta_r = \theta_i = 35°
The law of reflection states that the angle of incidence equals the angle of reflection, measured from the normal to the surface. This applies to all types of waves.

Example 2

medium
A light ray strikes a mirror. The angle between the incident ray and the reflected ray is 80°80°. What is the angle of incidence?

Example 3

medium
Two plane mirrors meet at 90°90°. A ray strikes the first mirror at 25°25° to the normal. After reflecting off both mirrors, by what total angle has the ray's direction been deflected?

Example 4

medium
A plane mirror rotates by 5°5°. By how many degrees does a fixed incident ray's reflected ray rotate?

Example 5

hard
A person 1.8 m1.8 \text{ m} tall stands 2 m2 \text{ m} from a vertical plane mirror. How tall must the mirror be (minimum) for the person to see their full reflection? Where should its top edge be?

Example 6

hard
Two plane mirrors meet at 60°60°. A ray enters parallel to one mirror and reflects off the other. After reflecting off the second mirror, then the first, what angle does the outgoing ray make with the incoming ray?

Example 7

medium
A ray reflects off mirror A at 35°35° from normal, then hits mirror B (perpendicular to A) at 55°55° from A's surface. Verify the angle of incidence on B equals 55°55° from B's normal.

Example 8

hard
A periscope uses two parallel mirrors, each tilted 45°45° from horizontal. A horizontal ray enters the top mirror. What is the direction of the ray exiting the bottom mirror?

Example 9

challenge
Three mutually perpendicular mirrors form a corner cube. Show that any ray entering the corner cube exits parallel to (but reversed from) the incoming ray.

Example 10

medium
A ray reflects off a mirror, then off a second mirror parallel to the first. What can you say about the outgoing ray's direction relative to the incoming ray's direction?

Example 11

hard
A ray hits a concave spherical mirror at a point where the local surface normal makes 10°10° with the principal axis. The incoming ray is parallel to the principal axis. After reflection, at what angle to the axis does the ray travel?

Example 12

medium
A ray makes 40°40° with mirror A's surface. Mirror B is rotated 15°15° away from A in the same plane. The ray reflects off A, then strikes B. What is the angle of incidence on B?

Example 13

challenge
An observer at point PP wants to send a light signal to a target at TT via a single mirror reflection on line LL. Describe how to find the reflection point on LL using the image-of-PP trick.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A ray of light hits a smooth surface at an angle of 0°0° to the normal (perpendicular). What happens?

Example 2

medium
A concave mirror has a focal length of 15 cm15 \text{ cm}. An object is placed 30 cm30 \text{ cm} from the mirror. Use the mirror equation 1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} to find the image distance. Is the image real or virtual?

Example 3

easy
Light strikes a mirror at an angle of incidence of 30∘30^\circ from the normal. Find the angle of reflection.

Example 4

easy
In the law of reflection, angles are measured from what reference line?

Example 5

easy
Light hits a mirror along the normal (angle of incidence 0∘0^\circ). What is the angle of reflection?

Example 6

easy
Does reflection change the wavelength of a wave?

Example 7

easy
Light reflects off a mirror with an angle of incidence of 45∘45^\circ. Find the angle of reflection.

Example 8

easy
What kind of reflection occurs off a smooth mirror, producing a clear image?

Example 9

easy
What kind of reflection occurs off a rough surface like paper, scattering light?

Example 10

easy
An incident ray makes 20∘20^\circ with the mirror surface. Find the angle of incidence from the normal.

Example 11

medium
A ray reflects off a mirror; the angle between the incident and reflected rays is 80∘80^\circ. Find the angle of incidence.

Example 12

medium
A horizontal ray hits a mirror tilted so its normal is 30∘30^\circ from horizontal. By what angle is the ray deflected?

Example 13

medium
Two mirrors meet at 90∘90^\circ. A ray reflects off both. By what total angle is it deflected?

Example 14

medium
A ray strikes a mirror at θi=25∘\theta_i = 25^\circ. The mirror is then rotated by 10∘10^\circ. By how much does the reflected ray rotate?

Example 15

medium
Light reflects off a vertical mirror, then a horizontal mirror (a periscope-like setup). A downward-then-... actually a ray going right hits a 45∘45^\circ mirror. What angle does it leave at relative to its original path?

Example 16

medium
A ray reflects with angle of reflection 35∘35^\circ. What is the angle between the reflected ray and the mirror surface?

Example 17

medium
A ball-like wave pulse reflects off a wall at θi=60∘\theta_i = 60^\circ. After reflection, what is \theta_r and does the speed change?

Example 18

medium
A ray hits a mirror at θi=15∘\theta_i = 15^\circ. Find the angle between the reflected ray and the incident ray.

Example 19

medium
A vertical ray travels upward and reflects off a mirror so it then travels horizontally. What is the angle of incidence from the normal?

Example 20

challenge
Two mirrors meet at an angle of 60∘60^\circ. How many images of an object placed between them are formed?

Example 21

challenge
A ray travels horizontally and must be turned to travel straight up using one flat mirror. At what angle to the horizontal must the mirror be set?

Example 22

challenge
A ray reflects off mirror 1 (\theta_i = 30 degrees), then hits mirror 2 placed parallel to mirror 1. Show the final ray is parallel to the incoming ray.

Example 23

easy
A laser pointer hits a plane mirror at 20°20° to the normal. What is the angle of reflection?

Example 24

easy
A light ray hits a plane mirror at 48°48° to the normal. What is the angle between the incident and reflected rays?

Example 25

medium
A horizontal light ray strikes a mirror tilted 30°30° from vertical. At what angle below horizontal does the reflected ray travel?

Example 26

medium
A ray hits a plane mirror at 52°52° from the surface. What is the angle of reflection from the normal?

Example 27

easy
A vertical light ray strikes a horizontal mirror on the floor. In what direction does it reflect?

Example 28

easy
Light hits a mirror with angle of incidence 15°15°. The angle between the reflected ray and the mirror surface is?

Example 29

medium
A water wave reflects from a barrier. The incident wavefronts approach at 30°30° to the barrier. At what angle do the reflected wavefronts move away from the barrier?

Example 30

medium
Light from a small bulb 1.0 m1.0 \text{ m} above a flat horizontal mirror creates a virtual image. Where is the image?

Example 31

medium
A light ray strikes a mirror; the angle of reflection is measured as 62°62°. What is the angle of incidence?

Example 32

medium
Sound from a clap reflects off a cliff 170 m170 \text{ m} away. How long until the echo returns? (Use speed of sound 340 m/s340 \text{ m/s}.)
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Background Knowledge

These ideas may be useful before you work through the harder examples.

waves