A student wants to achieve a total magnification of x400 using a microscope with a x10 eyepiece. What should be the magnification of the objective lens?

The total magnification of a compound microscope is the product of the eyepiece magnification and the objective lens magnification.

$$\text{Total Magnification} = \text{Eyepiece Magnification} \times \text{Objective Lens Magnification}$$

We are given:

• Desired Total Magnification = $\times 400$
• Eyepiece Magnification = $\times 10$ Let $M_{objective}$ be the objective lens magnification.

$$400 = 10 \times M_{objective}$$

Divide both sides by 10:

$$M_{objective} = \frac{400}{10}$$ $$M_{objective} = 40$$

The calculated objective lens magnification is $\times 40$. This matches one of the options.

The correct option is x40.

$$\text{x40}$$