Light: Reflection and Mirrors

What you will learn

Use a ray diagram and a signed calculation to answer the same question: where does a mirror form an image, and what is that image like? You will distinguish reflection from image formation, choose useful rays, and connect a mirror's use with the object's position. This is secondary-level optics practice within General Science, not a prediction of topic-wise exam marks.

1 Light and the ray model

An object is visible when light from it enters the eye. A lamp emits light; a book is usually seen by the light it reflects. Light can travel through vacuum; its vacuum speed is approximately 3 × 10⁸ m/s.

In a homogeneous transparent medium, where optical properties do not vary from place to place, the school-level ray model represents light travelling in straight lines. A ray is a line with an arrow showing the direction of travel, not a material thread. This model works well when wave effects such as diffraction are negligible. It does not mean that light can never change direction: it can reflect at a surface or refract between media.

2 Reflection uses the normal

At the point where a ray strikes a surface, draw a perpendicular to that surface. This line is the normal. On a spherical mirror, the local normal passes through the centre of curvature.

The angle of incidence i is measured between the incoming ray and the normal. The angle of reflection r is measured between the outgoing ray and the same normal. The laws are:

• i = r
• The incident ray, reflected ray and normal at the point of incidence lie in one plane

Worked angle example: A ray makes 35° with a plane mirror's surface. Its angle with the normal is 90° − 35° = 55°. Therefore i = r = 55°, not 35°. The reflected ray also makes 35° with the surface. Draw the normal before substituting an angle.

A smooth surface can reflect a parallel beam in one regular direction. A rough surface has different local normals, so the reflected rays spread in different directions. This diffuse reflection still obeys the reflection laws at each point. It is not a failure of i = r.

3 Real and virtual images

A real image is formed where the outgoing rays actually meet. A suitably placed screen can receive it. A virtual image is located where the backward extensions of outgoing rays meet; the rays do not actually pass through that apparent point. Such an image cannot be caught directly on a screen there, though an eye or camera can see it by receiving the outgoing light.

Use solid lines with arrows for actual ray paths and dashed lines for backward extensions. “Virtual” does not mean invisible. “Real” does not mean necessarily larger.

4 A plane mirror

For a real object in front of a plane mirror, the image is virtual, erect and equal in size to the object. Its perpendicular distance behind the mirror equals the object's perpendicular distance in front. The familiar left-right reversal in a mirror is called lateral inversion; the mirror does not turn the image upside down.

Worked distance example: A marker is 1.8 m in front of a stationary plane mirror. Its image is 1.8 m behind it, so marker-to-image separation is 3.6 m. Move the marker 0.3 m towards the mirror: the new distances are 1.5 m on each side and the separation is 3.0 m. The separation decreases by 0.6 m. Keep “distance from the mirror” separate from “distance between object and image”.

To construct a plane-mirror image, send two rays from the same object point to different mirror points, reflect each with equal angles to its local normal, and extend the reflected rays backwards. Their extensions intersect at the corresponding image point behind the mirror.

5 Spherical mirrors and their landmarks

A concave mirror has its reflecting face curved inward; a convex mirror reflects from the outward-bulging face. Both are parts of a sphere in our model.

• P, the pole, is the middle point of the reflecting surface
• C, the centre of curvature, is the centre of the sphere of which the mirror is a part
• The principal axis is the straight line through P and C
• R is the signed distance PC, the radius of curvature
• F is the principal focus. Rays parallel and close to the axis converge there after reflection from a concave mirror, or appear to come from it after reflection from a convex mirror
• f is the signed distance PF, the focal length

For spherical mirrors in the paraxial approximation, f = R/2. Paraxial rays remain near the principal axis and make small angles with it. Do not extend this relation into a claim that every wide beam striking a spherical mirror meets at exactly one point. The ray constructions and mirror equation below use the same idealized approximation.

6 Construct the image with two rays

Start both rays at the tip of the same upright object. For a concave mirror, one useful ray travels parallel to the axis and reflects through F. A second ray aimed through C returns along its own path because it strikes along the normal. Alternatively, a ray through F reflects parallel to the axis, or a ray striking P reflects at an equal angle to the axis. Their meeting point is the image tip.

For a convex mirror, a parallel incident ray reflects as if it came from F behind the mirror. A ray aimed towards C is reflected back along its incoming line. The actual reflected rays diverge; their dashed backward extensions meet behind the mirror. Do not draw the solid reflected rays travelling through the mirror to that virtual image.

For real objects on the principal-axis side facing a concave mirror, the main cases are:

• Object beyond C: image between C and F, real, inverted, smaller
• Object at C: image at C, real, inverted, same size
• Object between C and F: image beyond C, real, inverted, larger
• Object at F: outgoing rays from a point are parallel; no image at a finite distance in this ideal model
• Object between F and P: image behind the mirror, virtual, erect, larger
• Very distant object: image approaches the focal plane; an on-axis distant point is imaged near F

For a finite real object in front of a convex mirror, the image lies behind the mirror between P and F. It is virtual, erect and diminished. The real-object condition matters; this is not a statement about every possible converging incident beam. As a real object becomes very distant, its image approaches F.

7 Cartesian signs before calculation

Draw incident light travelling from left to right, with the object on the left. Take P as the origin. Measure all distances from P, never from F or C.

• Right of P is positive; left of P is negative
• Height above the axis is positive; height below is negative
• For the real objects here, u is negative
• Concave mirror: f and R are negative; convex mirror: f and R are positive
• A real mirror image in front has v negative; a virtual image behind has v positive

Write the values with their signs before using the mirror equation: 1/f = 1/v + 1/u, so 1/v = 1/f − 1/u.

Here u is object distance, v image distance, and f focal length. Use one consistent length unit. Signed linear magnification is m = h′/h = −v/u, where h and h′ are object and image heights. The sign tells orientation: positive means erect and negative means inverted relative to an upright object. The magnitude |m| tells size: above 1 enlarged, below 1 diminished, and 1 equal size.

8 Three signed calculations

Example 1 Concave mirror and a screen: An upright 4 cm object is 36 cm in front of a concave mirror whose focal length has magnitude 12 cm.

u = −36 cm; f = −12 cm; h = +4 cm. 1/v = −1/12 − (−1/36) = −3/36 + 1/36 = −1/18. Thus v = −18 cm. The image is 18 cm in front of the mirror, where a screen can receive it. m = −(−18)/(−36) = −1/2, so h′ = (−1/2) × 4 = −2 cm. It is real, inverted and half-size. Check the position: C is 24 cm in front; an object beyond C should form its image between C and F, as 18 cm does.

Example 2 Concave mirror used close up: Put an object 10 cm in front of a concave mirror with focal-length magnitude 15 cm.

u = −10 cm; f = −15 cm. 1/v = −1/15 − (−1/10) = (−2 + 3)/30 = 1/30. Thus v = +30 cm and m = −30/(−10) = +3. The image is 30 cm behind the mirror, virtual, erect and three times as tall. The object is inside the focal length. Do not place a screen 30 cm in front merely because “30” is the answer; its sign locates the image.

Example 3 Convex mirror: Put an object 30 cm in front of a convex mirror with f = +20 cm.

u = −30 cm. 1/v = 1/20 − (−1/30) = 3/60 + 2/60 = 1/12. Thus v = +12 cm and m = −12/(−30) = +0.4. The image is virtual, erect and 0.4 times the object's height. It lies between P and F behind the mirror, matching the ray construction.

9 Choose a mirror by what it does

A convex traffic or vehicle mirror gives a wider field of view and smaller erect images of real objects. A concave shaving or dentist's mirror gives an enlarged erect image when the object is between P and F. A concave reflector sends light approximately parallel when a small source is near its focus; this is the school model behind a torch reflector. Concentrating nearly parallel sunlight near a focus is the reverse path. Real devices may use shapes other than spherical mirrors, so the model explains the principle rather than every design detail. Never look at the Sun directly or into focused sunlight.

10 Practice before reading the key

1. A ray makes 25° with a plane mirror surface. What is its reflection angle measured from the normal?

A. 25° B. 50° C. 65° D. 75°

2. A real object is 0.8 m in front of a plane mirror. What is the object–image separation?

A. 0.4 m B. 0.8 m C. 1.6 m D. 2.4 m

3. Which statement about diffuse reflection is correct?

A. The reflection law fails at rough surfaces B. Local normals differ, but each ray obeys i = r C. Every reflected ray travels parallel to the others D. A rough surface absorbs all incident light

4. An upright real object is between F and P of a concave mirror. Which image is obtained in the paraxial model?

A. Real, inverted and smaller B. Real, erect and larger C. Virtual, inverted and smaller D. Virtual, erect and larger

5. A concave mirror has u = −40 cm and f = −10 cm. Find v using the mirror equation.

A. −40/3 cm B. +40/3 cm C. −8 cm D. +8 cm

6. A convex mirror forms a virtual image with u = −24 cm and v = +8 cm. What is its signed magnification?

A. −3 B. +3 C. −1/3 D. +1/3

11 Explained key

1. C. The incidence angle is 90° − 25° = 65°, so the reflection angle is 65°. The given surface angle is not i.

2. C. The image is 0.8 m behind the mirror. The total separation is 0.8 + 0.8 = 1.6 m.

3. B. Different local surface orientations spread the reflected beam. They do not change the local law. Neither parallel output nor total absorption follows.

4. D. Inside the concave focal length, reflected rays diverge and their backward extensions meet behind the mirror: the image is virtual, erect and enlarged.

5. A. 1/v = −1/10 − (−1/40) = −3/40, hence v = −40/3 cm. The negative sign places the real image in front; using the lens equation would give a different result.

6. D. m = −v/u = −8/(−24) = +1/3. It is erect and one-third as tall. Reversing the ratio gives 3; dropping the mirror minus sign gives −1/3.

Sources and next step

NCERT Science Chapter 9, Light Reflection and Refraction, reprint 2026–27, §§9.1–9.2.4, printed pp.134–145, supplies the secondary-level reflection, image and formula framework. NCERT Physics Part II Chapter 9, §§9.2.1–9.2.3, pp.222–226, makes the paraxial condition explicit. The teaching, numbers and practice here are original. Continue with Refraction and Lenses to compare what changes when light passes through, rather than reflects from, an optical element.

Analogy

Use a ray construction rather than a bouncing-ball analogy. Put a point object to the left of a plane mirror. Draw two incident rays, then use i = r at each point. Extend only the reflected rays backwards with dashed lines. The extensions meet at a point equally far behind the mirror. This shows why the image can be seen without light physically coming through the mirror from that point.

Quick reference

Quick reference

• Measure i and r from the normal; i = r even in diffuse reflection
• Plane mirror: for a real object, virtual, erect, equal size; equal perpendicular object and image distances
• Use the paraxial spherical-mirror model: f = R/2; 1/f = 1/v + 1/u
• Incident light left to right: real object u < 0; concave f < 0; convex f > 0
• Mirror magnification m = −v/u; sign gives orientation, |m| gives size
• Concave: a real object inside F gives an enlarged virtual erect image; outside F gives a real inverted image
• Convex: a finite real object gives a virtual erect diminished image between P and F behind the mirror
• Check signs, location and image size against the ray construction