Question

For the same objective . what is the ratio of the least separation between two points to be distinguished by a microscope for light of 5000Å and electrons accelerated through 100V used as an illuminating substance?

• A. 3075
• B. 3575
• C. 4075
• D. 5075

Answer 1

Answer: (C)

4075

Answer 2

The limit of resolution of a microscope is $d = \frac{\lambda}{2\sin\theta}$ where $2\theta$ is the angle of cone of light rays entering the objective of the microscope.

Here, $\lambda_{1} = 5000Å$

For electrons accelerated through 100 V, de Broglie wavelength,

$\lambda_{2} = \frac{12.27}{\sqrt{100}}Å = 1.227Å$

As $(2\sin\theta)$ is same in the two cases, therefore,

$\frac{d_{1}}{d_{2}} = \frac{\lambda_{1}}{\lambda_{2}} = \frac{5000}{1.227} = 4075$