1aReflection and Mirrors
Explore the law of reflection, plane and curved mirrors, and use the mirror equation to locate and describe images.
Mirrors are everywhere — from bathroom mirrors to telescopes to laser systems. Understanding reflection and the mirror equation lets you predict exactly where an image will form and how it will look.
Lesson Overview
When light strikes a surface it bounces back — this is reflection. In this lesson you will learn the law of reflection, explore how plane, concave, and convex mirrors form images, and apply the mirror equation and magnification formula to solve quantitative problems.
Key Concepts
Law of Reflection
The angle of incidence equals the angle of reflection (θᵢ = θᵣ), both measured from the normal.
Plane Mirror
Flat mirror that produces a virtual, upright, same-size image located as far behind the mirror as the object is in front.
Concave Mirror
Curved inward (converging) mirror; can produce real or virtual images depending on object distance.
Convex Mirror
Curved outward (diverging) mirror; always produces a virtual, upright, diminished image.
Mirror Equation
1/f = 1/dₒ + 1/dᵢ relates focal length, object distance, and image distance.
Magnification
m = −dᵢ/dₒ; negative m means inverted image, |m| > 1 means enlarged.
A ray of light strikes a plane mirror at an angle of incidence of 35°. What is the angle of reflection?
An object is placed 20 cm in front of a concave mirror with a focal length of 8 cm. Find the image distance.
Using the result from Example 2, find the magnification and describe the image.
An object is 30 cm in front of a convex mirror with focal length −15 cm. Find the image distance and magnification.
A concave mirror produces a real, inverted image with magnification −2 when the object is 18 cm away. Find the focal length.
A ray hits a flat mirror at 50° to the mirror surface. What is the angle of reflection measured from the normal?
Hint: The angle of incidence is measured from the normal, not the surface. If the ray is 50° from the surface, it is 40° from the normal.
An object is placed at the focal point of a concave mirror (dₒ = f). What happens to the image?
Hint: Substitute dₒ = f into the mirror equation and see what dᵢ equals.
A concave mirror has f = 10 cm. Where must an object be placed to produce a virtual, upright image?
Hint: Virtual images in concave mirrors form when the object is inside the focal point (dₒ < f).
Why does a convex mirror always produce a virtual image regardless of object position?
Hint: For a convex mirror f is negative. Use the mirror equation and consider the sign of dᵢ.
A plane mirror shows your image 1.5 m behind the mirror. How far are you from the mirror?
Hint: For a plane mirror the image distance equals the object distance.
Key Vocabulary
Normal
An imaginary line perpendicular to a surface at the point of incidence; angles of incidence and reflection are measured from it.
Example: A ray hitting a mirror at 30° to the normal reflects at 30° to the normal on the other side.
Focal Length (f)
The distance from the mirror (or lens) to the focal point; positive for concave mirrors, negative for convex mirrors.
Example: A concave mirror with f = 12 cm converges parallel rays to a point 12 cm in front of it.
Real Image
An image formed where reflected rays actually converge; can be projected onto a screen; dᵢ is positive.
Example: A concave mirror forms a real image of a candle on a wall when the candle is beyond the focal point.
Virtual Image
An image formed where reflected rays appear to diverge from; cannot be projected; dᵢ is negative.
Example: A plane mirror always forms a virtual image behind the mirror surface.
Interactive Practice — 5 Questions
A light ray strikes a mirror at 42° to the normal. What is the angle of reflection?
Which type of mirror always produces a virtual, upright, diminished image?
An object is 24 cm from a concave mirror with f = 8 cm. What is the image distance?
A magnification of −3 means the image is:
For a plane mirror, which statement is correct?
Independent Practice
A ray strikes a mirror at 28° to the mirror surface. Find the angle of incidence and the angle of reflection.
An object is 40 cm from a concave mirror with f = 10 cm. Calculate dᵢ and m, and describe the image.
A convex mirror has f = −20 cm. An object is 60 cm away. Find dᵢ and m.
Explain why rear-view mirrors in cars are convex rather than concave.
★ A concave mirror produces an image with m = −4 at dᵢ = 80 cm. Find dₒ and f, then verify using the mirror equation.
ChallengeCommon Mistakes
Measuring the angle of incidence from the mirror surface instead of the normal.
Always measure θᵢ and θᵣ from the normal (perpendicular) to the surface.
Forgetting that convex mirrors have a negative focal length in the mirror equation.
For convex mirrors f < 0; substitute the negative value directly into 1/f = 1/dₒ + 1/dᵢ.
Assuming a negative image distance means the image is behind the observer.
Negative dᵢ means the image is behind the mirror (virtual); positive dᵢ means in front (real).
Math Tips
Mirror equation tip: find a common denominator when solving 1/dᵢ = 1/f − 1/dₒ. Multiply both sides by f·dₒ·dᵢ to clear fractions if algebra gets messy.
Sign convention: distances measured in the direction of incoming light (in front of mirror) are positive; behind the mirror are negative.