Spherical Mirrors & Lenses
(NSO – Physics – Quick‑Study Notes)
1. Simple Explanation
| Item | What it is | How it works |
|---|---|---|
| Spherical mirror | A mirror whose reflecting surface is a section of a sphere. | Light rays that strike the surface are reflected according to the law of reflection. The curvature causes the reflected rays to converge or diverge. |
| Spherical lens | A transparent lens whose surfaces are sections of spheres. | Light rays that pass through the lens are refracted (bent) by Snell’s law. The curvature makes the rays converge or diverge. |
| Image | The point where light rays appear to come from (real) or where they appear to disappear into (virtual). | The image can be magnified, reduced, inverted, or upright, depending on the geometry. |
2. Key Points
| Concept | Mirror | Lens |
|---|---|---|
| Principal axis | Straight line through the centre of curvature and the centre of the mirror. | Same concept; passes through the lens centre. |
| Focal point (F) | Point where parallel rays (incoming from the left) reflect to converge (convex) or appear to diverge (concave). | Point where parallel rays (incoming from the left) converge (convex) or appear to diverge (concave). |
| Focal length (f) | Distance from mirror centre to F. | Same. |
| Radius of curvature (R) | Distance from mirror centre to centre of curvature. f = R/2 for a spherical mirror. |
Same: f = R/2 for a thin spherical lens. |
| Sign convention | 1. Do (object distance) is positive if the object is on the incoming side (left side). 2. Di (image distance) is positive if the image is on the right side of the mirror (i.e., on the outgoing side). 3. f is positive for concave mirrors and converging lenses; negative for convex mirrors and diverging lenses. | Same as above. |
| Mirror equation | (\displaystyle \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}) | (\displaystyle \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}) |
| Lens equation | Same as mirror equation (for thin lenses). | Same. |
| Magnification (m) | (m = -\frac{d_i}{d_o}) | (m = -\frac{d_i}{d_o}) |
| Image nature | Real & inverted if (d_i>0); virtual & upright if (d_i<0). | Real & inverted if (d_i>0); virtual & upright if (d_i<0). |
| Ray diagram rules | 1. Principal ray: parallel to axis → reflected through F. 2. Focal ray: through F → reflected parallel to axis. 3. Central ray: through centre of curvature → reflected straight back. | 1. Principal ray: parallel to axis → refracted through F. 2. Focal ray: through F → refracted parallel to axis. 3. Central ray: through centre of lens → passes undeviated. |
3. Worked Example
Example 1 – Concave Mirror
Given
- Focal length (f = +10;\text{cm}) (concave).
- Object distance (d_o = +30;\text{cm}).
Find
- Image distance (d_i).
- Magnification (m).
- Nature of the image.
Solution
-
Mirror equation
[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \quad\Rightarrow\quad \frac{1}{10} = \frac{1}{30} + \frac{1}{d_i} ] -
Compute (1/d_i):
[