Exit Angle & N2: Solving 26°-64°-90° Prism Problem

[DrMcDreamy]

Homework Statement

This is a two part problem:

2) As shown in the figure, a light ray is incident normally on one face of a 26◦–64◦–90◦ block of dense flint glass (a prism) that immersed in water. Find the exit angle θ4 of the light ray (Assume the index of grass is 1.69, and that of water is 1.333.) Answer in units of ◦.

3) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal reflection cease at point P ?

Homework Equations

n₁sin$$\theta$$₁=n₂sin$$\theta$$₂

The Attempt at a Solution

My work:

I put in the answer to number 2 and it said its wrong. What I am doing wrong? Can you guys guide me through the problem? TIA!

 

[DrMcDreamy]

Anybody?!

 

[rl.bhat]

In problem 2, theta3 = 180 - (26 + 26 + 90)

 

[DrMcDreamy]

So it would be:

$$\theta$$₃=180-(26+26+90)=38$$\circ$$

n₃sin$$\theta$$₃=n₄sin$$\theta$$₄
1.69sin38=1.33sin$$\theta$$₄
$$\frac{1.0405}{1.33}$$=sin$$\theta$$₄
sin^-10.7823=$$\theta$$₄
51=$$\theta$$₄

And #3 is right? TIA

 

[DrMcDreamy]

*bump*

 

[SammyS]

It looks OK.