• Plane mirror: Image is virtual, erect, same size and laterally inverted. Image distance = object distance.
• Minimum mirror height to see full self-image = half the person’s height.
• Multiple images with two mirrors: If angle between mirrors \(A\), number of images \(n=\dfrac{360^\circ}{A}-1\) (for exact divisibility).
• Spherical mirrors: Concave (converging/focusing); Convex (diverging/dispersion). Terms: P, C, R, principal axis, F, \(f=\dfrac{R}{2}\).
• Ray rules (concave/convex): (1) Parallel → through F. (2) Through F → Parallel. (3) Through C → retraces path.
• Convex mirror images: Always behind mirror, virtual, erect, diminished—used in vehicles’ side mirrors & wide-view mirrors.
• Concave mirror images: Depend on object position; can be real/virtual; used in shaving mirror, dentist mirror, torches, headlamps, solar devices.
• Sign convention (Cartesian): Object on left \(\Rightarrow u<0\); real image on left \(\Rightarrow v<0\); convex \(f>0\), concave \(f<0\); upward \(+\), downward \(-\).
• Mirror formula: \(\displaystyle \frac{1}{v}+\frac{1}{u}=\frac{1}{f}\) (valid for all spherical mirrors).
• Magnification: \(\displaystyle M=\frac{h_2}{h_1}=-\frac{v}{u}\). \(M>0\) → erect (virtual), \(M<0\) → inverted (real).

1) What is a mirror?

A reflecting surface that forms clear images.

2) Who first made a silvered glass mirror?

Justus von Liebig.

3) Lateral inversion happens in which mirror?

Plane mirror.

4) Minimum mirror height to see full image?

Half of the person’s height.

5) Formula for number of images with two mirrors at angle \(A\)?

\(n=\dfrac{360^\circ}{A}-1\) (when \(360^\circ/A\) is integer).

6) Which mirror converges light?

Concave mirror.

7) Which mirror always gives diminished, erect, virtual images?

Convex mirror.

8) Relation between \(R\) and \(f\)?

\(f=\dfrac{R}{2}\).

9) Write mirror formula.

\( \frac{1}{v}+\frac{1}{u}=\frac{1}{f}\).

10) Magnification formula.

\(M=\dfrac{h_2}{h_1}=-\dfrac{v}{u}\).

11) Sign of \(f\) for concave mirror?

Negative.

12) Sign of \(f\) for convex mirror?

Positive.

13) What kind of image forms at focus for distant object in concave?

Real, inverted, very small (point-like) at F.

14) Image by convex mirror for any object distance?

Virtual, erect, diminished behind mirror.

15) Principal axis is?

Line through pole and centre of curvature.

16) Centre of curvature is?

Centre of the sphere of which mirror is a part.

17) Name two uses of concave mirror.

Shaving mirror, headlights/torches, solar concentrators.

18) Name two uses of convex mirror.

Vehicle side mirrors, wide-angle shop mirrors.

19) Which mirror in “laughing chamber” causes distorted images?

Curved mirrors (concave/convex of varying curvature).

20) Real image can be obtained on?

A screen.

1) Define incident and reflected rays.

Incident: ray striking mirror; Reflected: ray leaving mirror after reflection.

2) State the law of reflection.

Angle of incidence = angle of reflection; incident ray, reflected ray and normal lie in one plane.

3) For plane mirror, image distance equals?

Object distance (perpendicular to mirror).

4) What is principal focus (concave)?

Point where rays parallel to principal axis meet after reflection.

5) What is principal focus (convex)?

Point behind mirror from which reflected rays appear to diverge.

6) Define focal length.

Distance between pole and principal focus.

7) Write relation between \(u,v,f\).

\( \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\).

8) When is magnification positive?

For erect virtual images.

9) When is magnification negative?

For inverted real images.

10) Which mirror gives wider field of view?

Convex mirror.

11) Which mirror can form a real enlarged image?

Concave (object between F and C).

12) What is lateral inversion?

Left–right reversal in plane mirror images.

13) Nature of image at C (concave) for object at C?

Real, inverted, same size at C.

14) What happens to image as object moves from infinity to C (concave)?

From tiny at F to same size at C, always real and inverted.

15) Source position in a torch using concave mirror?

At focus to obtain parallel beam.

16) Which mirror used by dentists and why?

Concave; gives magnified erect virtual image when object is between P and F.

17) Sign of \(u\) for an object placed in front of mirror (left)?

Negative.

18) If \(M=\dfrac{h_2}{h_1}=1\), what does it infer?

Image size equals object size (e.g., concave at C or plane mirror).

19) What is a real image?

Formed by actual convergence of rays; can be caught on screen; inverted.

20) What is a virtual image?

Apparent intersection; cannot be caught on screen; erect.

1) Why is a plane mirror image laterally inverted?

Because image forms behind mirror at equal perpendicular distance; left–right gets swapped with respect to normal.

2) State and explain the three ray rules for spherical mirrors.

Parallel→through F; through F→parallel; through C→retraces path—each comes from equality of incidence and reflection angles.

3) Explain why convex mirrors are preferred as rear-view mirrors.

They provide a wider field of view; images are erect though diminished, helping drivers see more area behind.

4) Give two uses of concave mirrors with object positions.

Shaving/dentist mirrors: object between P and F → erect magnified virtual image. Torches/headlamps: source at F → parallel beam.

5) Define focal length and radius of curvature; give relation.

\(f\): P–F distance; \(R\): C–P distance; relation \(f=\dfrac{R}{2}\).

6) Write the Cartesian sign convention for mirrors.

Object on left: \(u<0\); rightward distances \(+\); upward \(+\), downward \(−\); concave \(f<0\), convex \(f>0\).

7) Derive magnification \(M=-\dfrac{v}{u}\).

From similar triangles in ray diagram: \(\dfrac{h_2}{h_1}=\dfrac{-v}{u}\), negative sign accounts for inversion when image is real.

8) What image do you get when object is at infinity for a concave mirror?

A tiny real inverted image at the focus (point image).

9) Describe divergence vs convergence using mirrors.

Concave reflects parallel rays to converge at F; convex reflects them to diverge as if from F behind mirror.

10) Why do solar devices use concave mirrors?

They concentrate sunlight at/near focus, increasing energy density (heating/cooking).

11) How to identify concave vs convex mirror experimentally?

Bring mirror close to face—concave gives enlarged erect; moving away flips to inverted; convex always gives smaller erect image.

12) Explain “minimum mirror height = half the person’s height”.

By geometry, rays from head and feet meet mirror at midpoints between eyes and ends; required segment equals half height.

13) What happens to image in concave mirror as object moves from C to F?

Image moves from C to infinity, enlarging progressively (real, inverted) and at F becomes very large (at infinity).

14) State nature/position of image when object is between F and P (concave).

Virtual, erect, magnified behind the mirror.

15) Write mirror formula and conditions of validity.

\(\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\); valid for paraxial rays and spherical mirrors for all object positions.

16) Why do street lights use dispersing setup?

To spread light over area; a divergent beam (convex mirror/reflector) helps distribute light widely.

17) Give two daily-life examples of lateral inversion.

Ambulance word appears reversed in rear-view; mirrored selfies show swapped logos/text.

18) How can a concave mirror burn paper with sunlight?

Sun’s parallel rays converge at focus; energy concentrated there raises temperature enough to char/burn paper.

19) If \(M=2\) for a mirror image, what does it mean?

Image is twice as tall as object (if positive → erect virtual; if negative → inverted real).

20) Why do convex mirrors seem to make objects “closer than they appear”?

Because they diminish images; brain interprets smaller size as farther away, so mirrors warn that objects are actually closer.

1 a) Explain plane, concave and convex mirrors w.r.t. type & size of images.

Plane: Virtual, erect, same size, laterally inverted. Concave: Can be real/inverted (size varies: enlarged at between F and C; same at C; diminished beyond C) or virtual/erect & magnified (object between P and F). Convex: Always virtual, erect, diminished behind mirror.

1 b) Source positions in: (1) Torch (2) Projector lamp (3) Floodlight (using concave mirror)

(1) Torch: source at focus → parallel beam. (2) Projector/Headlamp: filament at/near focus → strong beam forward. (3) Floodlight: source a little beyond centre of curvature → bright concentrated beam (as given in text).

1 c) Why are concave mirrors used in solar devices?

They concentrate parallel sunlight at focus, increasing intensity and temperature for heating/cooking/solar furnaces.

1 d) Why are outside car mirrors convex?

They provide a wider field of view and give erect images; though diminished, more area is visible for safety.

1 e) Why does a concave mirror burn paper with the Sun?

Sun’s parallel rays are focused at F; high energy concentration raises temperature enough to burn paper.

1 f) If a spherical mirror breaks, what about the pieces?

Each piece behaves as a smaller spherical mirror of the same type and same radius/focal length (locally), but with its own pole and principal axis.

2) What sign conventions are used for spherical mirrors?

Pole as origin; principal axis as +X to the right. Distances right of P positive, left negative; upward positive, downward negative; object on left ⇒ \(u<0\); concave \(f<0\), convex \(f>0\).

3) Draw ray diagrams for concave mirror (all six standard cases).

Use the three rules: parallel↔focus; through F↔parallel; through C↔same path. (Students to practice diagrams.)

4) Which mirrors are used in: Periscope, Floodlights, Shaving mirror, Kaleidoscope, Street lights, Car headlamps?

Periscope – plane; Floodlights – concave; Shaving – concave; Kaleidoscope – plane; Street lights – convex (for divergence/wide spread); Headlamps – concave.

5 a) An object \(h_1=7\text{ cm}\) at \(u=-25\text{ cm}\) in front of a concave mirror of \(f=-15\text{ cm}\). Find \(v\) and image size & nature.

Using \( \frac{1}{v}+\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}= -\frac{1}{15}+\frac{1}{25}=-\frac{2}{75}\Rightarrow v=-37.5\text{ cm}\). \(M=-\frac{v}{u}=-\frac{-37.5}{-25}=-1.5\Rightarrow h_2=Mh_1=-10.5\text{ cm}\). Screen at 37.5 cm; image real, inverted, 10.5 cm.

5 b) A convex mirror has \(f=+18\text{ cm}\). Image is half of object. Find object distance.

For erect image, \(M=+\frac{1}{2}=-\frac{v}{u}\Rightarrow v=-\frac{u}{2}\). Mirror formula: \(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\Rightarrow -\frac{2}{u}+\frac{1}{u}=\frac{1}{18}\Rightarrow -\frac{1}{u}=\frac{1}{18}\Rightarrow u=-18\text{ cm}\). Object is 18 cm in front.

5 c) A 10 cm stick before a concave mirror \(f=10\text{ cm}\); nearer end at 20 cm. Find image length.

Given answer (text): 10 cm. (Using standard treatment for this configuration as in textbook solutions.)

6) Three mirrors from one sphere—what is common (P, C, R, principal axis)?

Common: same centre of curvature \(C\) and radius \(R\). Not common: each piece has its own pole \(P\) and principal axis through its own pole.

• Mirror formula: \(\displaystyle \frac{1}{v}+\frac{1}{u}=\frac{1}{f}\)
• Focal relation: \(\displaystyle f=\frac{R}{2}\)
• Magnification: \(\displaystyle M=\frac{h_2}{h_1}=-\frac{v}{u}\)
• Multiple images (two mirrors angle \(A\)): \(\displaystyle n=\frac{360^\circ}{A}-1\) (if \(\tfrac{360^\circ}{A}\) integer)