NEB Class 11 • Physics • Geometrical Optics

Reflection at Curved Mirrors: NEB Class 11 Physics Guide

Use the law of reflection to build concave and convex mirror ray diagrams, then make the mirror formula, sign convention and magnification agree with the image.

Principal axis, focus and radius of curvature
Ray diagrams, mirror formula and magnification
Image cases, applications and worked examples

Ray diagrams and equations must describe the same image.

Curriculum boundary

What Reflection at Curved Mirrors includes

The CDC secondary curriculum specifies the relation among object distance, image distance and focal length, image-size relation, focal-length calculations and applications. Check the CDC Physics Grade 11 page for the current Nepal resource.

This guide follows the law of reflection in OpenStax reflection and the paraxial spherical-mirror treatment in OpenStax image formation by mirrors.

Mirror geometry

Name every principal point

Pole P: geometric centre of the reflecting surface.
Principal axis: line through P and centre of curvature C.
Centre of curvature C: centre of the sphere of which the mirror is a part.
Radius R: distance PC.
Principal focus F: point where paraxial parallel rays converge or appear to diverge.
Focal length f: distance PF, with magnitude R/2 for a paraxial spherical mirror.

Concave and convex describe the reflecting surface. A real image forms where reflected rays actually meet and can be projected; a virtual image forms where backward extensions appear to meet and cannot be projected on a screen.

Construction rules

Three reliable principal rays

A ray parallel to the principal axis reflects through F for a concave mirror, or appears to come from F for a convex mirror.
A ray through or directed toward F reflects parallel to the axis.
A ray through or directed toward C returns along its path because it strikes normally.

Two accurate rays locate the image; a third checks the construction. Draw arrowheads, use a ruler, distinguish solid real rays from dashed backward extensions and start rays from the same object point.

The law of reflection requires angles measured from the local normal, not the mirror surface. At a spherical surface, the radius toward C is the normal at the point of incidence.

Concave and convex cases

Predict image nature before calculation

Mirror/object position	Image	Nature
Concave, beyond C	Between C and F	Real, inverted, diminished
Concave, at C	At C	Real, inverted, same size
Concave, between C and F	Beyond C	Real, inverted, enlarged
Concave, at F	At infinity ideally	Reflected rays parallel
Concave, inside F	Behind mirror	Virtual, upright, enlarged
Convex, any real object	Behind mirror between P and F	Virtual, upright, diminished

This table is a prediction tool, not a substitute for a diagram. If an equation result contradicts the predicted region, revisit signs and arithmetic.

Quantitative model

Mirror formula, focal length and magnification

Many texts write 1/f=1/u+1/v or 1/f=1/d_o+1/d_i, with signs depending on the declared convention. Magnification relates heights and distances, commonly m=h_i/h_o=−v/u in a real-is-positive convention. Use the convention taught by your school or source and define it before substitution.

For a paraxial spherical mirror, f=R/2. This approximation fails for large-aperture rays far from the principal axis, where spherical aberration prevents all parallel rays from meeting at one point.

Consistency check: the sign of magnification should match orientation; |m| greater than one means enlarged and less than one means diminished.

Worked examples

Concave and convex mirror calculations

Concave mirror, object beyond C

Using the real-is-positive magnitude form, f=10 cm and u=30 cm. 1/v=1/10−1/30=1/15, so v=15 cm. Image lies between F and C, is real and inverted. m=−15/30=−0.50.

Concave mirror, object inside focus

Let f=10 cm and u=6 cm. The signed result places v behind the mirror; in a real-is-positive convention v=fu/(u−f)=60/(−4)=−15 cm. m=−v/u=+2.5: virtual, upright and enlarged.

Convex mirror

For a convex mirror with f=−20 cm and real object u=40 cm in this convention, 1/v=1/f−1/u=−1/20−1/40=−3/40, so v≈−13.3 cm. m≈+0.333: virtual, upright and diminished.

Find radius

A concave mirror focuses distant paraxial rays 25 cm from its pole. f=25 cm, so R=50 cm.

Uses and design trade-offs

Why different curved mirrors are chosen

Concave close-up

Inside the focus it gives an upright enlarged virtual image, useful for examination.

Reflector

A source near F produces approximately parallel reflected rays.

Convex security

A wide field of view is gained with diminished virtual images.

Telescope

Large concave mirrors collect and focus light without chromatic aberration.

Real devices also involve aperture, aberrations, surface quality and alignment. The simple mirror equation is a paraxial first model.

Practical method

Find focal length of a concave mirror

For a distant object, place a screen in front of the concave mirror and adjust until a sharp diminished image forms. Measure pole-to-screen distance as an estimate of f. Never use the Sun; choose a safe distant object and avoid bright sources.

Repeat with different distant objects, measure from the pole rather than mirror stand, reduce parallax and report the spread. A large mirror aperture can blur the focus; use a paraxial stop if provided. For a fuller u–v method, measure several object and image distances and analyse the chosen mirror relation.

Use PhET Geometric Optics only after predicting the ray path and verify that the selected simulation mode matches mirrors.

Exam routine

Seven steps for every mirror problem

Identify concave or convex and mark P, F and C.
Place object relative to F and C.
Predict image region, orientation and size.
State the sign convention.
Draw two principal rays.
Apply mirror and magnification relations.
Compare result with the prediction.

Common errors include angles measured from the surface, rays starting from different object points, missing dashed virtual extensions, switching sign conventions and accepting an image in the wrong region. Review Vectors Study Guide if direction conventions are weak and Physical Quantities for unit discipline.

For online or physical NEB tuition, call 9846662070.

Practice tasks

Closed-book mirror checkpoint

Define P, F, C, R and f.
Draw three principal rays for each mirror.
Complete all concave image cases.
Explain why a convex image is always virtual for a real object.
Solve three mirror-formula questions.
Use magnification to identify orientation and size.
Explain f=R/2 limits.
Evaluate a focal-length experiment.

Frequently asked questions

Questions about curved mirrors

Where are reflection angles measured?

From the normal at the point of incidence, not from the mirror surface.

Why is f approximately R/2?

For paraxial rays on a spherical mirror, geometry and the law of reflection give the principal focus halfway to the centre of curvature.

Can a concave mirror form a virtual image?

Yes, when a real object is placed between the pole and principal focus.

What image does a convex mirror form?

For a real object it forms a virtual, upright and diminished image behind the mirror between P and F.

How do I avoid sign mistakes?

State one convention, predict the image from a ray diagram and use that convention consistently in every relation.

Where can I get NEB curved-mirror help?

For current online or physical tuition options, call 9846662070 and confirm timetable, class mode, teacher availability and fees.

References and next steps

Sources and related study guides

Continue through the Class 11 Physics revision roadmap and interleave ray diagrams with numerical practice. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Paraxial limitation

Why wide spherical mirrors blur a focus

Rays far from the principal axis strike a spherical mirror at geometry that makes them meet the axis at different positions from paraxial rays. This spherical aberration means a large aperture may not produce a single sharp focus. Restricting the aperture improves paraxial agreement but reduces collected light.

A parabolic reflector can bring parallel axial rays closer to one focus, which is why real optical design goes beyond the elementary spherical relation. In NEB problems, state the paraxial assumption unless the question provides a different model.

Construction quality

How to make a ray diagram measurable

Choose a scale that places P, F, C, object and expected image on the page. Use a sharp pencil and ruler; rays must start from one object point. After locating the intersection, measure u, v and heights and compare the diagram magnification with the formula. Differences should be discussed as drawing uncertainty, not hidden by moving the image arrow.

For a virtual image, extend reflected rays backward with dashed lines only. Keep the real reflected rays solid and point arrowheads in the propagation direction.

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