# Refractive index to measure temperature

1. May 24, 2006

Here is the question:
A factory uses a beam of light to allow workers to visually check the temperature of a liquid. A semi-circular crown glass (refractive index (n) =1.75) block is placed in a liquid X whose refractive index n changes with temperature T (in °C) according to the formula:
n = 2.25 – 0.025T
A light ray may be directed to the centre of the glass block makes and angle Ө = 60° with the normal

If the ray is totally reflected at O, find the refractive index and the corresponding temperature of liquid X.

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My working:
$$\theta_{critical}=\frac{n_{1}}{n_{2}}$$
from this point onwards I am stuck, any post regarding hints/working/solution will be greatly appreciated
Thank you,

2. May 24, 2006

### Exotic-Matter

well, it's sin(theta_c)=n2/n1 , ( n1>n2 )

try working this out, with givens you have.

3. May 25, 2006