Question

A spherical surface of radius R separates two medium of refractive indices µ₁ and µ₂, as shown in figure. Where should an object be placed in the medium 1 so that a real image is formed in medium 2 at the same distance?

Options

• `((mu_2-mu_1)/(mu_2+mu_1))`R

• `((mu_2+mu_1)/(mu_2-mu_1))`R

• `((mu_2+mu_1)/mu_2)`R

• `(mu_2/(mu_2+mu_1))`R

Answer 1

`bb(((mu_2+mu_1)/(mu_2-mu_1))"R")`

Explanation:

µ₁ = Refractive index of object medium

µ₂ = Refractive index of image medium

R = Radius of curvature

`mu_2/"v"-mu_1/"u" = (mu_2-mu_1)/"R"`

`mu_2/x-mu_1/-x= (mu_2-mu_1)/"R"`

`(mu_1+mu_2)/x = (mu_2-mu_1)/"R"`

⇒ x = `((mu_2+mu_1)/(mu_2-mu_1))`R