A liquid lies on top of the horizontal surface of a block of glass. A ray of light traveling in the glass has speed 1.85 x 10^8 m/s, wavelength 365 nm, and frequency 5.07x 10^14 Hz. The ray is incident on the surface of the glass at an angle of 38.0° with respect to the normal to the surface. The ray that refracts into the liquid makes an angle of 44.7° with the normal to the interface between the two materials.
a) What is the speed of the light when it is traveling in the liquid?
b)What is the wavelength of the light when it is traveling in the liquid?
c)What is the frequency of the light when it is traveling in the liquid?

(a) velocity of light in liquid = 2.09 x 10^8 m/s

(b) Wavelength in liquid = 42.35 nm

(c) remains same  

Explanation:

Speed of light in glass, v = 1.85 x 10^8 m/s

wavelength in glass, λg = 365 nm

frequency, f = 5.07 x 10^14 Hz

angle of incidence on glass surface, i = 38°

angle of refraction on liquid surface, r = 44.7°

(a)

According to the Snell's law

where,  g μ l is the refractive index of liquid with respect to water

Sin 38° / Sin 44.7° = 1.85 x 10^8 / velocity of light in liquid

0.886 = 1.85 x 10^8 / velocity of light in liquid

velocity of light in liquid = 2.09 x 10^8 m/s

(b)

velocity of light in glass/ velocity of light in liquid =  λg / λl

365 / λl = 1.85 / 2.09

λl = 412.35 nm

Wavelength in liquid = 42.35 nm

(c)

frequency of light remains unchanged as it is the property of source, it cant be changed due to reflection or refraction.

0.11 m/s and 0.28 m/s should be correct

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