Understanding Optical Microscope Magnification

The magnification of an optical microscope, specifically a compound microscope, is determined by the combined magnification of its two main lens systems: the objective lens and the eyepiece (or ocular lens).

The total magnification (\(M\)) of a compound microscope is the product of the magnification of the objective lens (\(M_o\)) and the magnification of the eyepiece (\(M_e\)):

\[ M = M_o \times M_e \]

Let's look at how the magnification of each lens system is determined:

• Objective Lens Magnification (\(M_o\)): The magnification of the objective lens is approximately given by the ratio of the tube length (\(L\), the distance between the objective and eyepiece) to the focal length of the objective lens (\(f_o\)). \[ M_o \approx \frac{L}{f_o} \] This shows that the objective magnification increases as its focal length decreases.
• Eyepiece Magnification (\(M_e\)): The eyepiece acts like a magnifying glass for the intermediate image formed by the objective. For viewing a final image at infinity (relaxed eye), the magnification is given by the ratio of the near point distance (\(D\), approximately 25 cm for a normal eye) to the focal length of the eyepiece (\(f_e\)). \[ M_e = \frac{D}{f_e} \] This shows that the eyepiece magnification increases as its focal length decreases.

Since the total magnification is the product of \(M_o\) and \(M_e\), and \(M_e\) is inversely proportional to the focal length of the eyepiece (\(f_e\)), the total magnification (\(M\)) will also be inversely proportional to the focal length of the eyepiece.

\[ M = M_o \times \frac{D}{f_e} \] Thus, if the focal length of the eyepiece (\(f_e\)) increases, the eyepiece magnification (\(M_e\)) decreases, and consequently, the total magnification (\(M\)) of the optical microscope decreases.

Analyzing the Options

Let's evaluate the given statements based on our understanding of optical microscope magnification:

• Option 1: Magnification increases with the increase in focal length of eyepiece
  This statement is incorrect because magnification decreases as eyepiece focal length increases (\(M_e \propto 1/f_e\)).
• Option 2: Magnification increases with the increase in focal length of objective
  This statement is incorrect because objective magnification decreases as its focal length increases (\(M_o \propto 1/f_o\)).
• Option 3: Magnification does not depend upon the focal length of eyepiece
  This statement is incorrect because magnification is directly dependent on the eyepiece focal length, specifically it is inversely proportional to it.
• Option 4: Magnification decreases with the increase in focal length of eyepiece
  This statement is correct. As derived from the formula \(M_e = D/f_e\), an increase in \(f_e\) leads to a decrease in \(M_e\), and therefore a decrease in total magnification \(M\).

Summary of Relationship

Therefore, the correct statement is that magnification decreases with the increase in focal length of the eyepiece.

Revision Table: Optical Microscope Magnification

Additional Information: Optical Microscope Components

An optical microscope uses a system of lenses to produce magnified images of small objects. The two main lens systems are:

• Objective Lens: This is the lens closest to the specimen. Microscopes usually have several objective lenses with different magnifications (e.g., 4x, 10x, 40x, 100x), which correspond to different focal lengths. Higher magnification objectives have shorter focal lengths.
• Eyepiece (Ocular Lens): This is the lens closest to the observer's eye. Eyepieces also come in different magnifications (e.g., 5x, 10x, 15x). Higher magnification eyepieces have shorter focal lengths.

By combining different objective and eyepiece lenses, varying total magnifications can be achieved.