In a compound microscope, the intermediate image is:
A. Virtual, erect and magnified
B. Real, erect and magnified
C. Real, inverted and magnified
D. Virtual, erect and reduced

Hint: First, understand the working of the compound microscope. Find out what kind of lenses are used in the compound microscope. By knowing the types of lenses, find out the nature intermediate image formed in a compound microscope.

Complete step by step solution:

We have to find the nature of the intermediate image formed by the compound microscope.
In a microscope, the lens having a smaller focal length placed near the object is known as the objective lens and the lens having a larger focal length placed near the eye of an observer is known as the eyepiece.
From the above ray diagram, it is clear that an intermediate image is an image formed by an objective lens. An object is placed just beside the focus of an objective lens. We know that when an object is placed just beside the focus of the convex lens, a real, inverted, and magnified image is formed. Thus, as you can see in the ray diagram an intermediate image, MN, formed by the objective lens is a real inverted and magnified image. This intermediate image formed by an objective lens is used as an object for an eyepiece. And as you see, an eyepiece has a larger focal length and the intermediate image is formed near its focus, it further produces an enlarged image. As eyepiece is also a convex lens, it acts as a simple magnifier and does not re-invert the image, thus the final image produced is virtual and inverted.

Hence, the correct answer is option (C)

Note: A microscope is an instrument that is used for viewing enlarged or magnified images of very small objects. Any microscope is characterized by its magnifying power. Magnifying power measures how much an enlarged image can be formed using a given instrument. For example, if a microscope has magnification power \[1000X\]then the image would appear 1000 times larger than the actual size of the image. The total magnifying power of a microscope is equal to the combined magnifying power of each lens used. For example, if the objective has a magnifying power\[~10X\] and eyepiece has magnifying power \[100X\] then magnifying power of a microscope will be \[1000X\text{ }\left( 10\text{ }x\text{ }100 \right).\]