Reflection and Spherical Mirrors
~9 min read
- Laws of reflection: Angle of incidence = angle of reflection. Incident ray, reflected ray, normal are coplanar.
- Spherical mirrors: Concave (converging) and convex (diverging). Pole, focus, centre of curvature.
- Mirror formula: 1/v + 1/u = 1/f. Magnification m = -v/u.
Reflection from a mirror surface follows two laws. Spherical mirrors form images of various sizes and positions. NDA tests mirror formula and image characteristics.
Laws of Reflection
- 1st law: The incident ray, reflected ray, and normal to the surface at the point of incidence all lie in the same plane.
- 2nd law: Angle of incidence = angle of reflection (both measured from the normal).
- Plane mirror: image is virtual, upright, of same size as object, laterally inverted (left-right swap). Image distance = object distance.
Spherical Mirrors
- Concave mirror: Reflecting surface curves inward. Converges parallel rays at focus. Forms real or virtual images depending on object distance.
- Convex mirror: Reflecting surface curves outward. Diverges parallel rays. Always forms virtual, erect, diminished images.
- Key terms:
- Pole (P): Centre of the mirror's surface.
- Centre of curvature (C): Centre of the sphere of which mirror is part.
- Radius of curvature (R): Distance from P to C.
- Principal focus (F): Midpoint between P and C.
- Focal length (f): Distance from P to F. f = R/2.
Mirror Formula and Magnification
Mirror formula: 1/v + 1/u = 1/f
where u = object distance, v = image distance, f = focal length.
Sign convention (Cartesian, common in NCERT):
- Object always on left of mirror. Distances measured from pole.
- Distances measured in direction of incident light: +ve. Against: -ve.
- For concave mirror: f is -ve (in front). For convex mirror: f is +ve (behind).
Magnification: m = h'/h = -v/u.
- +ve magnification: erect, virtual image.
- -ve magnification: inverted, real image.
- |m| > 1: enlarged. |m| < 1: diminished.
Image Formation by Concave Mirror
| Object Position | Image |
|---|---|
| At infinity | At F. Highly diminished. Real, inverted. Used in: solar furnace |
| Beyond C | Between F and C. Diminished. Real, inverted |
| At C | At C. Same size. Real, inverted |
| Between C and F | Beyond C. Enlarged. Real, inverted. Used in: cinema projector |
| At F | At infinity. Highly enlarged |
| Between F and P | Behind mirror. Enlarged. Virtual, erect. Used in: shaving mirror, makeup, dentist mirror, headlights |
Applications
- Concave: Headlights of vehicles (light source at focus → parallel beam), shaving/makeup mirrors (close-up enlarged), solar cookers, telescopes (large concave mirrors), reflectors.
- Convex: Rear-view mirrors in vehicles (wider field of view, diminished image), security mirrors (shops), street-corner mirrors.
- Plane: Common mirrors, dressing mirrors, periscopes (with two plane mirrors).
NDA PYQ Examples
Q: A convex mirror is used as a rear-view mirror because it:
(a) Forms a real image (b) Has wider field of view and forms diminished image (c) Magnifies the image (d) Costs less
Answer: (b) Wider field of view and diminished image.
Q: For a concave mirror, when object is at focus, image is:
(a) At focus (b) At centre of curvature (c) At infinity (d) Behind mirror
Answer: (c) At infinity — highly magnified.
Q: Focal length of a spherical mirror is:
(a) Equal to radius of curvature (b) Half of radius of curvature (c) Twice of radius (d) Independent of curvature
Answer: (b) Half of radius of curvature: f = R/2.
Drill Reflection and Spherical Mirrors for NDA
NDA-pattern items on Reflection and Spherical Mirrors with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why do dentists use a concave mirror?
To get a magnified, erect image of a tooth. When the tooth is placed between the pole and focus of a concave mirror, the image is enlarged and virtual — useful for close examination.
Why do convex mirrors give a wider view?
Their curved surface diverges incoming rays, so light from a wider area can reach the mirror. The image is diminished but the field of view increases — useful in vehicle rear-view mirrors and security mirrors.
What is lateral inversion?
Left-right reversal seen in a plane mirror. Your left hand appears as right hand of your image. Caused by reflection — the front-to-back axis is reversed. The mirror does not actually flip left-right; it appears so because of how we perceive the image.
Why are headlights concave reflectors?
To produce parallel beams of light. The bulb is placed at the focus of a concave reflector. Reflected rays from the focus become parallel to the axis — a sharp, intense beam projected forward.
What is the difference between a real and virtual image?
Real image — formed where light rays actually converge after reflection/refraction. Can be projected on a screen. Inverted. Virtual image — formed where light rays appear to come from (extended backward). Cannot be projected. Erect.