The image formed by an objective of a compound microscope is
(a) virtual and diminished
(b) real and

Q: Why can't the objective lens form a virtual image?

A virtual image cannot be projected onto a screen or into space; it only appears to exist when you look through the lens. The compound microscope relies on the objective lens projecting a physical (real) image down the tube so the eyepiece can use it as its own object.

Q: What happens if we place the object exactly at the focus of the objective lens?

If the object is exactly at the focus ($u = f_o$), the refracted rays become perfectly parallel. The image would form at infinity. This is useless for a microscope because the image would never form inside the finite length of the microscope tube.

Q: The book's solution says the object is placed 'between its focus and lens'. Is that right?

No, that is a pedagogical error in the book's text. Placing an object between the focus and the optical center of a convex lens produces a virtual, erect, and enlarged image. For a compound microscope objective, the object must be placed just *outside* the focus (between $f_o$ and $2f_o$) to get a real, inverted, and enlarged image.

Q: Why is the image inverted? Doesn't that make looking at specimens confusing?

Yes, the final image in a standard compound microscope is inverted. However, for looking at cells, bacteria, or tissue samples, orientation usually doesn't matter. The massive gain in magnification is worth the trade-off of an upside-down image.

Q: Why does the objective lens have such a short focal length?

Magnification for a lens is roughly proportional to the tube length divided by the focal length ($m \approx L/f_o$). A very short focal length allows for a very high primary magnification within a reasonably sized microscope tube.

Question

The image formed by an objective of a compound microscope is

Options:

(A) virtual and diminished

(B) real and diminished

(C) real and enlarged

(D) virtual and enlarged

Sigma Percentile · Accepted Answer

### The Anatomy of a Compound Microscope

To truly appreciate the genius behind a compound microscope, we must understand its dual-lens architecture. A compound microscope employs two convex lenses to achieve massive magnification: the **objective lens** (the one closest to the object) and the **eyepiece** (the one you look through).

The objective lens has a very short focal length ($f_o$) and a small aperture. Its primary mission is to capture light from a tiny specimen and project a magnified, real image deep inside the microscope tube.

### The Role of the Objective Lens

For the microscope to work, the intermediate image created by the objective lens *must* be real. Why? Because a real image is physically projected into space, allowing the second lens (the eyepiece) to use it as an actual object.

To achieve this, where should we place the specimen?

If we place the object *inside* the focal length ($u < f_o$), the convex lens acts like a simple magnifying glass, producing a virtual, erect image on the same side. This is useless for a compound microscope because the image wouldn't travel down the tube to the eyepiece.

Therefore, the object is placed **just outside the focal point**, specifically between $f_o$ and $2f_o$.

### The Ray Diagram and Image Formation

Let's trace the geometry:
1. **Ray 1:** A ray from the top of the object travels parallel to the principal axis. Upon striking the convex objective lens, it refracts and passes exactly through the principal focus ($F_o$) on the other side.
2. **Ray 2:** A second ray from the top of the object passes straight through the optical center of the lens. It continues its journey completely undeviated.

These two rays converge and physically intersect on the other side of the lens, beyond $2F_o$. Because the light rays actually meet, the resulting image is **real**. Because it forms below the principal axis, it is **inverted**. And crucially, because the object was placed between $f$ and $2f$, the geometry dictates that the image is **enlarged**.

*(Note: Some textbook solutions mistakenly state that the object is placed "between its focus and lens". As we've just proved, placing the object there would yield a virtual image, which is incorrect for the objective lens of a compound microscope. The object must be strictly beyond the focus!)*

### The Final Verdict

The objective lens of a compound microscope forms an intermediate image that is **real and enlarged**. This perfectly sets the stage for the eyepiece to act as a simple magnifier, taking this real image and blowing it up into the massive, virtual final image that your eye sees.

Thus, the correct option is **(c)**.

Animated Solution for Physics - Optics: The image formed by an objective of a compound microscope is

Select Answer:

Visualized Solution

The Objective Lens Setup

Placing the Object

Tracing the First Ray

Tracing the Second Ray

Image Formation

Conclusion

The Sigma Insight: Optical Instruments

The Anatomy of a Compound Microscope

The Role of the Objective Lens

The Ray Diagram and Image Formation

The Final Verdict

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