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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:

[tex]\theta_{critical}=\frac{n_{1}}{n_{2}}[/tex]

from this point onwards I am stuck, any post regarding hints/working/solution will be greatly appreciated

Thank you,

Pavadrin

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# Refractive index to measure temperature

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