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Aadarsh 3 years ago The wavelength of light in two liquids "x" and "y" is 3500 angstroms and 7000 angstroms respectively. Find the critical angle of "x" relative to "y".

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1. apoorvk

You know the wavelengths of the red and violet, you can find relative refractive indices for two lights (by assuming yellow light as a constant). Then you can use the formula for critical angle, since you already have the refractive indices. (just calculate everything in terms of an assumed constant 'x', and in the end you'll find that the 'x' gets cancelled)

2. Aadarsh

Can you expalin the steps please?

3. Aadarsh

@Ishaan94 please try.

4. Ishaan94

You need to tell me what's critical angle?

5. Aadarsh

The angle of incidence for which the angle of refraction is 90 degrees is called "critical angle".

6. Ishaan94

Oh hmm, so relative reflective index must be $$\large n = \frac{\lambda_x}{\lambda_y}$$, right?

7. Aadarsh

ooooooooh Yeah!!!!

8. Aadarsh

But how?

9. Ishaan94

|dw:1334817280641:dw|$n = \frac{\sin\theta_i}{\sin \theta_r}$

10. Ishaan94

$$\theta_r \to 90 \implies \sin\theta_r \to1$$$\implies n = \sin\theta_i$

11. Ishaan94

Wow. Nice. Thankyou Aadarsh for posting it.

12. Aadarsh

Yeah. Got it. So, it is: $\sin 30 = 3500/7000 = 1/2$ So, answer = sin 30 degrees, rite?

13. Ishaan94

Yes, It is.

14. Aadarsh

Thanks Bhaiiiiiiiiijan!!!

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