An optical fibre consists of a core (refractive index $$n_1$$) surrounded by a cladding (refractive index $$n_2$$). A ray of light enters the fibre from air at an angle $$\theta$$ with the fibre axis. The maximum value of $$\theta$$ for which the ray can propagate down the fibre is

A

$$\sin^{-1}\sqrt{\frac{n_1}{n_2}}$$

B

$$\sin^{-1}\sqrt{\frac{n_2}{n_1}}$$

C

$$\sin^{-1}\sqrt{n_1^2 + n_2^2}$$

D

$$\sin^{-1}\sqrt{n_1^2 - n_2^2}$$