Question

The convex lens used in a simple microscope which has a magnification of 5. The image is formed at the least distance of distinct vision. What is the focal length of the lens?
A) 6.25cm
B) 4.25cm
C) 10.25cm
D) 5.58cm

Answer 1

Hint: We are provided with image formation of a convex lens in a microscope that is at least distance of distinct vision which is generally 25cm for normal human eyes.

Formula used:
$m=1+{\displaystyle \frac{D}{f}}$ (where m is the magnification, D is the least distance of distinct vision and f is the focal length)
Using the above relation we will find the focal length of the convex lens.

Complete step by step solution:
Let’s discuss some of the properties of convex lenses and simple microscopes first.
Optical lenses are generally made up of two spherical surfaces. Converging lens is called the convex lens which converges rays of the incident light parallel to the principal axis at one point; this is the reason converging lenses are used in microscope-like objects to focus minute particles. Convex lenses are thick at the middle and thin at the top.
Microscope: microscope is the instrument used to see objects which are too small to be seen by the naked eyes.
Now we will calculate the focal length of the lens.
$$\begin{gathered} \Rightarrow m=1+{\displaystyle \frac{D}{f}} \\ \Rightarrow 5=1+{\displaystyle \frac{25}{f}} \end{gathered}$$(we have used the formula mentioned in the hint above and substituted values)
$$\begin{gathered} \Rightarrow 5-1={\displaystyle \frac{25}{f}} \\ \Rightarrow 4={\displaystyle \frac{25}{f}} \\ \Rightarrow f={\displaystyle \frac{25}{4}} \end{gathered}$$(We have rearranged the terms and came to the equation of the focal length)
$\Rightarrow f=6.25cm$ (Focal length of the convex lens)

Option (A) is correct.

Note: Converging lens (convex lens) is used for making magnifying glasses, binoculars, microscope, telescopes, camera, eyeglasses (for correction of hypermetropia), flashlights, peepholes etc.
Diverging lenses (concave lenses) are called negative lenses because they do not focus the light at one point instead diverge it.