anonymous
  • anonymous
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".
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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apoorvk
  • 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)
anonymous
  • anonymous
Can you expalin the steps please?
anonymous
  • anonymous
@Ishaan94 please try.

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anonymous
  • anonymous
You need to tell me what's critical angle?
anonymous
  • anonymous
The angle of incidence for which the angle of refraction is 90 degrees is called "critical angle".
anonymous
  • anonymous
Oh hmm, so relative reflective index must be \(\large n = \frac{\lambda_x}{\lambda_y}\), right?
anonymous
  • anonymous
ooooooooh Yeah!!!!
anonymous
  • anonymous
But how?
anonymous
  • anonymous
|dw:1334817280641:dw|\[n = \frac{\sin\theta_i}{\sin \theta_r}\]
anonymous
  • anonymous
\(\theta_r \to 90 \implies \sin\theta_r \to1\)\[\implies n = \sin\theta_i\]
anonymous
  • anonymous
Wow. Nice. Thankyou Aadarsh for posting it.
anonymous
  • anonymous
Yeah. Got it. So, it is: \[\sin 30 = 3500/7000 = 1/2 \] So, answer = sin 30 degrees, rite?
anonymous
  • anonymous
Yes, It is.
anonymous
  • anonymous
Thanks Bhaiiiiiiiiijan!!!

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