In a compound microscope, the objective and the eye piece focal lengths are

1. Analyze the Question

The question asks for the characteristics of the focal lengths of the lenses used in a compound microscope. Specifically, it wants to know how the focal lengths of the objective lens and the eyepiece compare to each other.

2. Explain the Concept

A compound microscope is an optical instrument used to view very small objects. It consists of two converging (convex) lenses:

• The Objective Lens: This lens is placed close to the object being viewed. To produce a highly magnified real image, the object must be placed just outside the focal point of this lens. Therefore, the objective lens must have a very short focal length.
• The Eyepiece (Ocular): This lens acts as a simple magnifier for the image formed by the objective lens. To provide high magnification, it also requires a short focal length.

In summary, both lenses in a compound microscope are designed to be short-focal-length lenses to achieve the high levels of magnification required for microscopy.

3. Show the Solution

• Step 1: Identify the purpose of the microscope. It is designed to magnify tiny objects.
• Step 2: Recall the lens formula for magnification. Magnification is inversely proportional to the focal length ($M \approx \frac{L}{f_o} \times \frac{D}{f_e}$). To get a large magnification ($M$), the focal lengths of both the objective ($f_o$) and the eyepiece ($f_e$) must be small.
• Step 3: Compare this to a telescope. In a telescope, the objective lens has a long focal length to gather light from distant objects, but in a microscope, we need high power, which necessitates short focal lengths for both lenses.

4. Identify the Answer

Based on the principles of optics, both the objective and the eyepiece of a compound microscope have short focal lengths.

The correct option is C.

5. Tip

Memory Trick: Think of the word "Micro" (meaning small). Since a microscope is for "micro" things, remember that the lenses must be "short" (small focal lengths). Conversely, for a telescope (used for "macro" or distant things), the objective lens is "long."