Because the objective lens of compound microscope has smaller focal length than the object distance so that a real inverted and magnificent image is formed in the intermediate stage

Introduction:
A compound microscope is an optical instrument that is commonly used to magnify small objects or specimens. It consists of two lenses - the objective lens and the eyepiece. The intermediate image is formed by the objective lens and is observed through the eyepiece.

Main Body:
Real Image:
The intermediate image formed by the objective lens in a compound microscope is a real image. A real image is formed when light rays actually converge at a point after passing through a lens. In this case, the objective lens converges the light rays coming from the specimen to form a real image.

Inverted Image:
The real image formed by the objective lens is inverted. This means that the top of the object appears at the bottom of the image and vice versa. The inversion of the image is a result of the way light rays are refracted when passing through the lens.

Magnified Image:
The real image formed by the objective lens is also magnified. Magnification refers to the increase in size of an object when viewed through a lens. In a compound microscope, the objective lens has a shorter focal length than the eyepiece, which allows for greater magnification of the image.

Virtual Image:
The real image formed by the objective lens is then further magnified by the eyepiece. However, the eyepiece creates a virtual image, which is not formed by the actual convergence of light rays. A virtual image is formed when light rays appear to be coming from a point behind the lens. In the case of the compound microscope, the eyepiece creates a virtual image that is viewed by the observer.

Erect Image:
The virtual image formed by the eyepiece is erect, meaning that it is not inverted like the real image formed by the objective lens. The eyepiece corrects the inversion of the image and presents it in an upright position to the observer.

Diminished Image:
Although not mentioned in the question, it is worth noting that the virtual image formed by the eyepiece is also diminished in size compared to the real image formed by the objective lens. This is because the eyepiece has a shorter focal length and acts as a magnifying lens to further increase the apparent size of the image.

Conclusion:
In conclusion, the intermediate image formed in a compound microscope is a real, inverted, and magnified image by the objective lens. However, the eyepiece creates a virtual, erect, and further magnified image that is observed by the user.