A ray of light changes its wavelength from 6000 Å to 3000 Å, when it travels from one medium to another medium. What is the critical angle of the denser medium with respect to the rarer medium? [ Given sin 0 =0 , sin 30= `1/2` , sin 45 = `1/sqrt2` , sin 60 = `sqrt3/2`, sin 90=1 ]

Explanation

To find the critical angle of the denser medium with respect to the rarer medium when a ray of light changes its wavelength from 6000 Å to 3000 Å, we can follow these steps:

### Step 1: Understand the relationship between wavelength and speed of light
The speed of light in a medium is directly proportional to its wavelength. When light travels from one medium to another, its speed and wavelength change, while the frequency remains constant.

### Step 2: Define the wavelengths in the two media
Let:
- \( \lambda_1 = 6000 \, \text{Å} \) (wavelength in the rarer medium)
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