Question

With reference to the lens maker’s formula, answer the following questions:

1. Apply the formula (expression) of refraction at a single spherical surface to:
   1. refraction at the first spherical surface.
   2. refraction at the second spherical surface.
2. Combine these two expressions/equations to obtain an expression for the focal length of the lens.

Answer 1

i. a. `mu_2/v - mu_1/u = (mu_2 - mu_1)/R`

`mu_2/(v') - mu_1/u = (mu_2 - mu_1)/R_1`

b. `mu_1/v - mu_2/(-v') = (mu_1 - mu_2)/R_2`

ii. Adding the expressions:

`1/v - 1/u = (mu_2/mu_1 - 1) (1/R_1 - 1/R_2)`

For air, μ₁ = 1

`1/v - 1/u = (mu_2 - 1) (1/R_1 - 1/R_2)`

When u = ∞, v = f

`1/f  = (mu_2 - 1) (1/R_1 - 1/R_2)`