Question

Derive the equation for thin lens and obtain its magnification.

Answer 1

1. Let us consider an object OO′ of height h₁ placed on the principal axis with its height perpendicular to the principal axis.
2. The ray OP passing through the pole of the lens goes undefeated.
3. The inverted real image II’ formed has a height h₂.
4. The lateral or transverse magnification m is defined as the ratio of the height of the image to that of the object.
   m = `("II'")/("OO'")`
   
5. From the two similar triangles ∆ POO’ and PII’, we can write,
   `("II'")/("OO'") = "PI"/"PO"`
   Applying sign convention,
   `(-"h"_2)/"h"_1 = "v"/(- "u")`
6. Substituting this in equation for magnification,
   m = `(- "h"_2)/"h"_1 = "v"/"u"`
   After rearranging,
   m = `"h"_2/"h"_1 = "v"/"u"`
7. The magnification is negative for real image and positive for virtual image.
8. Magnification by combining the lens equation with the formula for magnification as,
   m = `"h"_2/"h"_1 = "f"/("f + u")` (or)
   m = `"h"_2/"h"_1 = ("f - v")/"f"`