Question

Light rays are incident from air on a block of glass (Refractive Index = 1.5). The reflected and refracted rays are perpendicular to each other. The ratio of the wavelengths of the refracted and reflected light is

• A. 0.66
• B. 0.11
• C. 0.44
• D. 0.22

Hint:

In refraction problems, use the refractive index and the condition of perpendicular rays to find the ratio of the wavelengths.

Answer 1

The Correct Option is A

Step 1: Use of the refractive index.
The refractive index \( n \) relates the wavelength of light in a medium to the wavelength in a vacuum (or air). The relationship is: \[ n = \frac{\text{Wavelength in air}}{\text{Wavelength in medium}} \] In this case, \( n = 1.5 \), and the refracted ray's wavelength will be shorter in the glass. The ratio of the wavelengths of the refracted and reflected light is found by considering the refracted wavelength divided by the reflected wavelength.
Step 2: Using the perpendicularity condition.
Since the reflected and refracted rays are perpendicular, this condition simplifies the calculations, and we find that the ratio of the wavelengths of the refracted and reflected light is: \[ \frac{\text{Wavelength of refracted light}}{\text{Wavelength of reflected light}} = 0.66 \] Step 3: Conclusion.
Thus, the ratio is 0.66, corresponding to option (A).