An optical fibre consists of a glass core of refractive index $$n_1$$ surrounded by a cladding of refractive index $$n_2<n_1$$. A beam of light enters one end of the fibre at $$P$$, from air at angle $$\theta$$ with the axis of fibre as shown in the figure. Choose the correct option or options.

Maximum value of $$\theta$$ for which a ray can travel down the fibre is $$\theta=\sin^{-1}\sqrt{n_1^2-n_2^2}$$

Maximum value of $$\theta$$ for which a ray can travel down the fibre is $$\theta=\cos^{-1}\sqrt{n_1^2-n_2^2}$$

If $$\theta=30^\circ$$ in air and $$n_1=1.50$$, then for reflection just at the critical angle the value of $$n_2$$ is $$\sqrt2$$

For an axial ray and a ray repeatedly reflected at the critical angle over axial length $$L$$, the time difference is $$\Delta t=\frac{n_1}{n_2}\frac{L}{c}(n_1-n_2)$$