Physics - Geometrical Optics Question with Solution | TestHub

The magnifying power of a simple microscope is given by $M=1+\frac{D}{f}$ or $M=\frac{D}{f}$.

The focal length of a lens is related to the refractive index by the lens maker's formula: $\frac{1}{f}=(\mu -1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$.

According to Cauchy's relation, the refractive index decreases with an increase in wavelength: $\mu =A+\frac{B}{{\lambda }^2}$.

Since the wavelength of red light is greater than that of blue light (${\lambda }_{\text{red}}>{\lambda }_{\text{blue}}$), the refractive index for red light is less than that for blue light (${\mu }_{\text{red}}<{\mu }_{\text{blue}}$).

Consequently, the focal length of the lens is greater for red light ($f_{\text{red}}>f_{\text{blue}}$).

Since magnifying power is inversely proportional to focal length, the magnifying power decreases when the light is changed from blue to red ($M_{\text{red}}<M_{\text{blue}}$).

Answer: decreases