Question

olelow light in a liquid is 2.4 x 10 m/s. Find the refractive index of the que
The wavelength of red light in sir is 7890 À what is the wavelength in glass (n = 1.57%
Ans. 1.25
An. 5260 A​

Answer 1

Given :

Speed of light in liquid = 2.4×10⁸ m/s

Wavelength of light in air = 7890

Refractive index of glass = 1.5

To Find :

Refractive index of liquid and speed of red light in glass.

Solution :

■ Refractive index of a medium is defined as the factor by which speed of light reduces as compared to the speed of light in vacuum.

$\bigstar\:\underline{\boxed{\bf{\purple{\n=\dfrac{speed\:of\:light\:in\:vacuum}{speed\:of\:light\:in\:medium}}}}}$

By substituting the given values,

➠ n = c / v

➠ n = (3×10⁸) / (2.4×10⁸)

➠ n = 1.25

■ Refractive index of medium is inversely proportional to the wavelength of light in that medium.

$:\implies\sf\:\dfrac{n_{air}}{n_{glass}}=\dfrac{\lambda_{glass}}{\lambda_{air}}$

$:\implies\sf\:\dfrac{1}{1.5}=\dfrac{\lambda_{glass}}{7890}$

$:\implies\sf\:\lambda_{glass}=\dfrac{7890}{1.5}$

$:\implies\:\underline{\boxed{\bf{\orange{\lambda_{glass}=5260\:A^{\circ}}}}}$