When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of `sin r` versus `sin i` is as shown. From this one can conclude that

(i) the velocity of light in second medium is `sqrt3` times the velocity of light in the first medium
(ii) the velocity of light in the first medium is `sqrt3` times the velocity of ligth in second medium
(iii) the critical angle of the two media is given by `sin i_C=1sqrt3`
(iv) the critical anlge of the two media is given by `sin i_C=1sqrt2`

Options

A. (i), (ii)
B. (ii), (iii)
C. (i), (iii)
D. (i), (iv)

Answer

B

Explanation

`(sinr)/(sini)=tan30^@=1/sqrt3`
`1xxsini=sqrt3sinr`
`mu_1sini=mu_2sinr`
`mu_1=1`, `mu_2=sqrt3`
`mu_2/mu_1=sqrt3impliesv_1/v_2=sqrt3` (Since `muprop1//v`)
(ii) is O.K.
Circle angle
`mu_2sinC=mu_1sin90^@`
`sinC=mu_1/mu_2=1/sqrt3impliesC=sin^-1(1//sqrt3)`
(iii) is O.K.