Ray Optics Practice Problems: Mirrors, Lenses, and Refraction

Overview

This article gives you a structured set of mirror and lens problems, refraction questions, and image formation physics review prompts that you can return to more than once. Instead of only showing final answers, it focuses on the habits that make optics problems manageable under time pressure.

For most introductory courses, ray optics questions fall into five recurring types:

• Plane mirror questions about image distance, orientation, and apparent motion.
• Spherical mirror questions using the mirror equation and magnification.
• Thin lens questions involving converging and diverging lenses, real and virtual images, and image size.
• Refraction at a boundary using Snell's law.
• Mixed review problems where you decide which model applies before calculating.

Keep these core physics formulas nearby as your optics cheat sheet:

• Mirror equation: 1/f = 1/do + 1/di
• Thin lens equation: 1/f = 1/do + 1/di
• Magnification: m = hi/ho = -di/do
• Snell's law: n1 sin(theta1) = n2 sin(theta2)

Use a consistent notation:

• do = object distance
• di = image distance
• f = focal length
• ho = object height
• hi = image height

If your class uses a different sign convention, match your teacher or textbook. The math is only helpful if it matches the conventions you are expected to use on quizzes and lab write-ups.

Practice problem 1: Plane mirror image distance

A student stands 2.0 m in front of a plane mirror. How far behind the mirror is the image, and what is the distance from the student to the image?

Solution: In a plane mirror, the image forms the same distance behind the mirror as the object is in front.

• Image distance behind mirror = 2.0 m
• Student-to-image distance = 2.0 m + 2.0 m = 4.0 m

Answer: 2.0 m behind the mirror; 4.0 m from student to image.

Practice problem 2: Concave mirror image location

An object is placed 30 cm in front of a concave mirror with focal length 10 cm. Find the image distance.

Solution:

Use 1/f = 1/do + 1/di

1/10 = 1/30 + 1/di

1/di = 1/10 - 1/30 = 3/30 - 1/30 = 2/30 = 1/15

di = 15 cm

Answer: The image forms 15 cm in front of the mirror.

Interpretation: Positive image distance for a concave mirror usually means a real image, so the image is inverted.

Practice problem 3: Mirror magnification

Using the previous problem, if the object height is 4.0 cm, what is the image height?

Solution:

m = -di/do = -15/30 = -0.5

hi = m ho = (-0.5)(4.0 cm) = -2.0 cm

Answer: hi = -2.0 cm

The negative sign means the image is inverted. Its size is half the object's height.

Practice problem 4: Convex mirror conceptual check

An object is placed in front of a convex mirror. Is the image real or virtual? Upright or inverted? Larger or smaller?

Solution: A convex mirror forms a virtual, upright, reduced image for any object position.

Answer: Virtual, upright, and smaller.

Practice problem 5: Converging lens image distance

A converging lens has focal length 12 cm. An object is 18 cm from the lens. Find the image distance.

Solution:

1/f = 1/do + 1/di

1/12 = 1/18 + 1/di

1/di = 1/12 - 1/18 = 3/36 - 2/36 = 1/36

di = 36 cm

Answer: The image forms 36 cm from the lens on the opposite side.

Because the image distance is positive for a converging lens in this setup, this is a real image.

Practice problem 6: Converging lens magnification

For the lens above, if the object height is 3.0 cm, find image height.

Solution:

m = -di/do = -36/18 = -2

hi = m ho = (-2)(3.0 cm) = -6.0 cm

Answer: hi = -6.0 cm

The image is inverted and twice as tall as the object.

Practice problem 7: Diverging lens classification

An object is placed 25 cm from a diverging lens with focal length -10 cm. Find the image distance.

Solution:

1/f = 1/do + 1/di

1/(-10) = 1/25 + 1/di

1/di = -1/10 - 1/25 = -5/50 - 2/50 = -7/50

di = -50/7 ≈ -7.1 cm

Answer: di ≈ -7.1 cm

The negative image distance indicates a virtual image on the same side as the object.

Practice problem 8: Refraction with Snell's law

Light passes from air into glass. Let n1 = 1.00, n2 = 1.50, and angle of incidence = 30 degrees. Find the angle of refraction.

Solution:

n1 sin(theta1) = n2 sin(theta2)

(1.00) sin 30° = (1.50) sin(theta2)

0.5 = 1.5 sin(theta2)

sin(theta2) = 0.333...

theta2 ≈ 19.5°

Answer: The refracted angle is about 19.5 degrees.

Check: Since light enters a higher-index medium, it bends toward the normal, so the refracted angle should be smaller than 30 degrees. That matches the result.

Maintenance cycle

If you want these optics problems with solutions to remain useful, revisit them in a short maintenance cycle instead of cramming once and forgetting them. Ray optics is especially sensitive to small errors in signs, diagrams, and interpretation, so spaced review matters.

A practical cycle looks like this:

1. First pass: Solve each problem slowly with notes and diagrams.
2. Second pass, 2 to 3 days later: Redo the same problems without looking at the worked steps.
3. Third pass, 1 week later: Mix mirrors, lenses, and refraction in random order.
4. Fourth pass before a test: Solve under timed conditions and explain each answer in words.

The reason this works is simple: most students do not lose points because the formulas are hidden from them. They lose points because they forget which formula applies, switch signs halfway through, or fail to notice that an answer is physically impossible. Repeated short review sessions reduce those errors.

To keep the article usable as a recurring physics study guide, sort your review into these mini-sets:

• Set A: Concept-only questions — classify images as real or virtual, upright or inverted, enlarged or reduced.
• Set B: Single-equation calculations — use the mirror or lens equation directly.
• Set C: Magnification questions — connect image distance to image size and orientation.
• Set D: Refraction questions — use Snell's law and check whether the ray bends toward or away from the normal.
• Set E: Mixed review — choose the correct model before calculating.

Teachers can also use this cycle to rotate warm-up problems, short quizzes, or homework refreshers. Students preparing for AP Physics help or college physics help can use the same cycle as a low-effort review system during larger units on waves and optics questions.

If you want to connect this review style to other topics, a similar pattern works well in Newton's Laws Practice Problems With Step-by-Step Answers, Momentum and Impulse Study Guide: Formulas, Collisions, and Common Mistakes, and DC Circuit Problems With Answers: Ohm's Law, Series, and Parallel. The study skill is the same even when the formulas change.

Signals that require updates

This topic is evergreen, but your personal practice bank should still be updated when your needs change. A good optics review page is not static; it should grow with your course level.

Here are clear signals that your ray optics practice problems need a refresh:

• You can compute answers but cannot describe the image. Add more conceptual classification questions.
• You keep missing sign conventions. Add a one-page sign summary at the top of your notes.
• You only recognize familiar numbers. Replace easy integers with less friendly values so the method matters more than memorized patterns.
• Your course has moved beyond one-step questions. Add mixed review combining diagrams, equations, and explanation.
• You are preparing for cumulative exams. Mix optics with mechanics and electricity so topic switching becomes normal.

Search intent can shift too. Sometimes students want basic image formation physics, while at other times they want fast exam review. If you are using this article as a repeat reference, update your own study version in one of two directions:

• Beginner update: More ray diagrams, more conceptual checkpoints, fewer algebra-heavy questions.
• Exam-prep update: More timed questions, fewer hints, and stronger emphasis on physical interpretation.

You should also update your problem bank when classroom language changes. Some instructors emphasize “object side” and “image side.” Others focus on principal rays. Others prefer sign tables. None of those approaches is wrong on its own, but your practice should match the language you will see on assignments and tests.

If you are building a broader review system, it also helps to pair optics with neighboring units. For example, students often study optics near electricity and waves, so you may want to bookmark Electric Field and Electric Potential Explained for Beginners or later move into Magnetism and Electromagnetic Induction Study Guide as your course advances.

Common issues

Most mistakes in mirror and lens problems are not advanced physics errors. They are setup errors. If you can diagnose them quickly, you will improve faster than by simply doing more problems.

1. Using the right formula with the wrong signs

Students often remember 1/f = 1/do + 1/di but forget that focal length and image distance can be positive or negative depending on the optical element and convention.

Fix: Before substituting numbers, label the element: concave mirror, convex mirror, converging lens, or diverging lens. Then decide the sign of f and what sign result you expect for di.

2. Ignoring what the answer means physically

If a refraction answer says the ray bends away from the normal when entering a higher-index material, or a diverging lens somehow produces a large real image in a basic setup, something is probably wrong.

Fix: Add a 5-second reasonableness check after every calculation.

3. Confusing real and virtual images

Students may calculate image distance correctly but misidentify whether the image can be projected onto a screen.

Fix: Link sign and meaning. In many standard classroom conventions, positive image distance for converging systems often corresponds to real images; negative image distance often corresponds to virtual images.

4. Losing the negative sign in magnification

The sign of magnification tells you about orientation. Many wrong answers come from reporting the size correctly but forgetting whether the image is upright or inverted.

Fix: Always write both the signed value and a short interpretation, such as “-2, inverted and twice as large.”

5. Memorizing diagrams without understanding object position

For concave mirrors and converging lenses, image behavior depends strongly on whether the object is inside the focal point, at twice the focal length, or beyond it.

Fix: Practice the same device with multiple object positions rather than one example only.

6. Treating Snell's law like pure button-pressing

Refraction questions are often easy numerically but still misread conceptually.

Fix: Before calculating, ask: Is light entering a higher or lower refractive index? Should the angle get smaller or larger?

These kinds of corrections make your study time more efficient. They also generalize well across the rest of your physics practice problems, whether you are solving mechanics questions or circuit analysis. Good habits in setup and interpretation matter everywhere.

When to revisit

Return to ray optics on a schedule, not only when you feel stuck. That is the most reliable way to turn a one-time homework topic into long-term test readiness.

Revisit this topic:

• After your first classroom introduction to lock in vocabulary and sign conventions.
• After your first graded assignment to correct patterns in your mistakes.
• One week before a quiz or unit test to rebuild speed and confidence.
• Before a cumulative midterm or final to make sure optics still feels familiar.
• Any time you start forgetting image behavior for mirrors and lenses.

Here is a simple action plan you can use right away:

1. Copy the four key formulas onto one page.
2. Solve two mirror problems, two lens problems, and one Snell's law problem.
3. For each answer, write one sentence describing the image in words.
4. Circle every error caused by setup rather than algebra.
5. Repeat the same set in three days without notes.

If you are studying with classmates, split the review: one person checks equations, one checks signs, and one checks physical interpretation. If you are teaching, keep a short rotating bank of optics problems with solutions so students see the same core patterns several times across the term.

The goal is not to collect dozens of unrelated optics questions. It is to build a dependable set of standard problems you can revisit whenever your course returns to image formation, refraction, or cumulative review. Used that way, a small bank of well-chosen ray optics practice problems becomes a lasting part of your physics study guide and a practical source of step-by-step physics solutions when you need a refresher.