IIT JEE , AIEEE Forum - Physics , Optics

rahul1993

easy question lets see who can solve it first

a light ray is falling at an angle of 45degrees with a surface of a clean slab of iceof thickness 1m and is refracted at an angle of 30degrees. calculate the time taken by the light rays to cross the slab.

speed of light in vacuum = $3*{10}^{8}$ meters per second

i'll give you the working if you need but first try it yourself !!!!!

(ans:5.44 nano-seconds)

payal1spark

i think the angles hvnt got to do nythin...
its 1/speed of light in ice i.e. 3 x 10*8 x 3/4
so 1.33/3 x 10*8 gives 4.43 nanosec

DON007

look.....

refractive index is = 1.414..........

now....

speed of light in the slab is = 3*10^8 / (1.414) = 2.1216 * 10 ^8

now time taken = 1 /( 2.1216 * 10 ^8)

= 4.7134 nano seconds......

hope its right...

thanks

DON

studyid

see the attached figure .

first of all the light ray undergoes refraction so the path of the light ray is changed in the glass slab .

now $\mu (refractive index of glass slab) = \frac{sin i}{sin r} = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} =\sqrt(2) = 1.4142 \approx 1.43$

and $\mu = \frac{c}{v} \:\:,where\:v\:is\:velocity\:of\:light\:in\:glass\:slab$

hence we find $v = 2.09 X 10^{8}$

now from the figure we find the inclined height (h, which is the actual path of the ray in slab) ,

$cos30 =\frac{1}{h}\:hence\:h=\frac{2}{\sqrt{3}}\approx1.154 m$

now $v(velocity of light in slab) =\frac{distance}{time\: taken\: to\: travel(t) }$

hence $t = \frac{1.154}{2.09X10^8}$

hence

I hope that answers the query ,

DON007

ya ...i think it is right..sorry if the answer is wrong...i have misinterpreted the question...................

sorry 4 it

if its wrong....

rahul1993

your ans was correct had the ray been falling perpendicular to the ice slab.So studyid is correct

oneyeartogo

now try another similar question posted by me

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