Spherical Mirrors (Concise Notes)
Spherical Mirrors
- Mirror whose reflecting surface is a part of a shperical surface
- Concave Mirror: Reflecting surface curved inward.
- Convex Mirror: Reflecting surface curved outward.
- Pole (P): Centre of the reflecting surface. Part of the spherical mirror.
- Aperture: the effective diameter of reflecting surface that allows light to enter and reflect.
- Centre of Curvature (C): The centre of the sphere not part of the mirror.
- Radius of Curvature (R): The radius of the sphere to which the mirror belongs.
- Principal Axis: A straight line passing through the pole and the centre of curvature.
- Principal Focus (F):
- In a concave mirror, the focal point is the point on the principal axis where incident rays parallel to the principal axis converge after reflection.
- In a convex mirror, the focal point is the point on the principal axis from which incident rays parallel to the principal axis appear to diverge after reflection.
- Focal Length (f): Distance between the pole and the principal focus (R = 2f) for small apertures)
- Point light – a source of infinite light rays. All follow laws of reflection.
- at least two such rays needed.
- Any two of the following (for concave mirror):
- A ray parallel to the principal axis passes through the principal focus.
- A ray passing through the principal focus emerges parallel to the principal axis.
- A ray passing through the centre of curvature goes back along (retraces) the same path.
- For a ray incident at the pole, the normal is its principal axis. Incident ray and reflected ray make same angle with it.
- Any two of the following (for convex mirror):
- A ray parallel to the principal axis appears to diverge from the principal focus.
- A ray directed towards the principal focus emerges parallel to the principal axis.
- A ray directed towards the centre of curvature goes back along the same path.
- For a ray incident at the pole, the normal is its principal axis. Incident ray and reflected ray make same angle with it.
Image formation by Concave Mirror – Position and Nature
| Position of Object | Position of Image | Size of Image | Nature of Image |
|---|---|---|---|
| At infinity | At focus (F) | Highly diminished, point-sized | Real and inverted |
| Beyond C | Between F and C | Diminished | Real and inverted |
| At C | At C | Same size | Real and inverted |
| Between C and F | Beyond C | Enlarged | Real and inverted |
| At F | At infinity | Highly enlarged | Real and inverted |
| Between P and F | Behind the mirror | Enlarged | Virtual and erect |
Image formation by Convex Mirror – Position and Nature
| Position of Object | Position of Image | Size of Image | Nature of Image |
|---|---|---|---|
| At infinity | At focus (F), behind mirror | Highly diminished, point-sized | Virtual and erect |
| Between infinity and Pole (P) | Between P and F, behind mirror | Diminished | Virtual and erect |
Uses of Concave Mirrors
- Used in torches, searchlights, and vehicle headlights for parallel beams.
- Used as shaving mirrors for an enlarged image.
- Used by dentists to see large images of teeth.
- Used in solar furnaces to concentrate sunlight.
Uses of Convex Mirrors
- Used as rear-view mirrors in vehicles due to:
- A convex mirror at Agra Fort provides a full-length image of the Taj Mahal.
- The pole (P) is taken as the origin.
- The principal axis is the x-axis.
- New Cartesian Sign Convention:
- Object is always placed to the left of the mirror.
- Distances parallel to the principal axis:
- Right of the origin (+x-axis) → Positive
- Left of the origin (-x-axis) → Negative
- Distances perpendicular to principal axis:
- Above the axis (+y-axis) → Positive
- Below the axis (-y-axis) → Negative
Mirror Formula
\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\]
- v: Image distance
- u: Object distance
- f: Focal length
- Valid for all spherical mirrors and object positions.
Magnification
\[m = \frac{\text{Height of Image} (h’)}{\text{Height of Object} (h)}-\frac{h’}{h} = -\frac{\text{Image Distance} (v)}{\text{Object Distance} (u)} = -\frac{v}{u}\]
- h’ (height of image):
- Positive for virtual images.
- Negative for real images.
- Interpretation of sign:
- Negative magnification → Real and inverted image.
- Positive magnification → Virtual and erect image.
For Reflection of Light, Click Here
Reference NCERT Books
