Reflection at Spherical Mirrors: Formula, Sign Convention and Magnification Class 12 Physics | Ray Optics and Optical Instruments

Understand it

A spherical mirror has a pole, principal axis, centre of curvature, radius of curvature and focus.
For paraxial rays, the object distance u, image distance v and focal length f are related by the mirror formula.
Concave mirrors can form real or virtual images depending on object position, while convex mirrors generally form virtual, erect and diminished images for real objects.
The Cartesian sign convention is essential: distances measured in the direction of incident light are positive and those opposite are negative.
In the usual mirror setup with incident light from left to right, object distance for a real object is negative.

Example

A concave mirror used in a shaving mirror gives a magnified upright image when the face is placed between the pole and focus. A convex mirror in a vehicle gives a wider field of view with a diminished virtual image.

Formula and rule

Mirror formula: 1/v + 1/u = 1/f.

Magnification: m = -v/u = image height/object height.

Here u, v and f are in metres or centimetres, but all distances must use the same unit.

Use this for paraxial rays reflected from spherical mirrors.

Concave mirror has f negative in the usual setup; convex mirror has f positive.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A concave mirror has f = -20 cm and an object is placed at u = -30 cm.

1Using 1/v + 1/u = 1/f: 1/v - 1/30 = -1/20, so 1/v = -1/20 + 1/30 = -1/60.
2Thus v = -60 cm.
3Magnification m = -v/u = -(-60)/(-30) = -2.
4The image is real, inverted and twice the object size.

Method you can reuse

Identify mirror type; write signs of u and f; apply 1/v + 1/u = 1/f; solve for v; calculate m = -v/u; use signs of v and m to state image position, nature and size.

Visual tip

Ray diagram should show pole P, principal axis, focus F, centre of curvature C, incident ray parallel to the axis reflecting through F, and ray through C retracing its path. For convex mirror, reflected rays diverge and their backward extensions meet behind the mirror.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is the focal length of a concave mirror usually taken as negative in the Cartesian sign convention?

Think first, then show answer

For a concave mirror with incident light taken from left to right, the focus lies in front of the mirror, opposite to the positive direction. Therefore its distance from the pole is measured negative, so f is negative.

Common wrong answer

For the worked example, a common wrong answer is v = +60 cm and m = +2 because u is wrongly taken as positive.

Don't mix this up

Students often put u as positive for a real object in front of a mirror, which changes the image distance and magnification sign.

Exam tip

Before using the formula, draw a small axis sketch and mark the signs of u, v and f. This prevents most mirror numerical errors.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It appears as sign-convention numericals, image nature questions, ray diagram questions, and assertion-reason items on why convex mirrors are used as rear-view mirrors.

1
Enough for 1 mark
Reflection at a spherical mirror is the change in direction of light after striking a concave or convex reflecting surface that is part of a sphere, forming images according to the laws of reflection and the mirror formula.
2
Add for 2 marks
Example: A concave mirror used in a shaving mirror gives a magnified upright image when the face is placed between the pole and focus. A convex mirror in a vehicle gives a wider field of view with a diminished virtual image.
3
Add for 3 marks
A spherical mirror has a pole, principal axis, centre of curvature, radius of curvature and focus.

Use the concept graph around this idea instead of revising it in isolation.

Refraction, Snell's Law and Total Internal Reflection

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Refraction at Spherical Surfaces and Lens Maker's Formula

Refraction at a spherical surface describes image formation when light passes between two media separated by a curved refracting boundary. The lens maker's formula gives the focal length of a thin lens in terms of refractive index and radii of curvature of its two surfaces.

Optical Instruments: Microscope and Telescope

Optical instruments use lenses or mirrors to increase the apparent size or resolving usefulness of objects. A microscope magnifies nearby small objects, while a telescope increases the angular size of distant objects.

Power of a Lens and Combination of Thin Lenses

Power of a lens is the measure of its ability to converge or diverge light, numerically equal to the reciprocal of focal length in metres.

Next: Refraction, Snell's Law and Total Internal Reflection Back to full mind map

Reflection at Spherical Mirrors: Formula, Sign Convention and Magnification

Understand it

See it worked out

Check yourself

Write it in the exam

Concept practice is coming soon

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Reflection at Spherical Mirrors: Formula, Sign Convention and Magnification

Understand it

See it worked out

Check yourself

Write it in the exam

Related concepts

Concept practice is coming soon

Help improve this page