[Physics] Refraction?

Question

1.

What is the critical angle for the light passing from diamond (Nd = 2.24) to water (Nw = 1.33)?

2.

An underwater driver looking up at an angle of 45 degrees at the surface of still water can see the horizon. What would the diver see if she looked up at the water surface at an angle of 60 degrees?

3.

The critical angle for lighting passing from crown glass to oleic acid is 73.8 degrees. What is the refractive inndex for oleic acid relative to crown glass?

Answer 1

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1) sinC=nw/nd=1.33/2.24=0.5937

C=sin-1(0.5937)

C=36* 25'

2)tan45=1, tan60=root3

Here tangent of angle can be taken as radius of horizon by height of water from his eyes.

As tan60 = root3, which implies that he sees root(3) times more the height.

3)sinC=No/Nc

No/Nc=sin(73.8*)=sin(73* 48')=0.9603

So, No/Nc=0.9603

cNo=0.9603 (No relative to Nc symbolically).

Answer 2

3. sinC = 1/n

sin73.8 = 1/n

n = 1.0413

Answer 3

critical angle = sin (lighter)/ sin( denser)

= sin1.33/sin2.24