Question

When the length of microscope tube increases, its magnifying power (A) decreases (B) increase (C) does not change (D) none of these

Short answer

When the length of the microscope tube (L) increases, the term L/\(f_o\) in the magnifying power formula \(M = (1+\frac{L}{f_o})(\frac{25cm}{f_e})\) will also increase, assuming that the focal length of the objective lens (\(f_o\)) remains constant. As a result, the magnifying power (M) will increase. The correct answer is (B) increase.

Step-by-step solution

Understand the formula for magnifying power of a microscope

The formula for the magnifying power (M) of a microscope is given by: \(M = (1+\frac{L}{f_o})(\frac{25cm}{f_e})\) where L is the length of the microscope tube, \(f_o\) is the focal length of the objective lens, and \(f_e\) is the focal length of the eyepiece (all in centimeters).

Analyze the effect of a change in tube length on magnifying power

According to the formula, M is proportional to 1+L/\(f_o\). If the length L of the microscope tube increases, the term L/\(f_o\) will also increase as long as the focal length of the objective lens (\(f_o\)) remains constant. Since the rest of the formula remains constant, the overall magnifying power will increase as well.

Identify the correct answer

Based on our analysis in Step 2, when the length of the microscope tube increases, the magnifying power of the microscope increases as well. So, the correct answer is: (B) increase

Key concepts

Optical Instruments

Optical instruments are tools that help us see things that are too small, too far, or otherwise invisible to the naked eye. Everyday examples include glasses, telescopes, and microscopes. Each of these instruments capitalize on the properties of lenses to bend and focus light in a useful way. By manipulating light, they can create magnified or clearer images of objects beyond our typical capability of seeing. Understanding how these instruments work allows us to enhance our ability to observe tiny details or distant objects, expanding both our everyday experiences and scientific discoveries.

• Glasses: Help correct vision by adjusting the way light enters the eye.
• Telescopes: Allow astronomers, and stargazers to view distant stars and planets.
• Microscopes: Enable researchers to examine small samples in great detail, such as cells or tiny organisms.

These instruments are essential in many scientific fields as they provide insights and connections that cannot be achieved through unaided human vision.

Magnifying Power Formula

The magnifying power formula helps determine how much larger an optical instrument will make an object appear. For compound microscopes, the formula is:
\[ M = \left(1 + \frac{L}{f_o}\right) \left(\frac{25\text{ cm}}{f_e}\right) \]
Here's what the variables mean:

• \(L\): Length of the microscope tube.
• \(f_o\): Focal length of the objective lens.
• \(f_e\): Focal length of the eyepiece.
• 25 cm: Standard near point distance for ease of vision.

Using this formula, you can see that the magnifying power depends on both the length of the tube (L) and the focal lengths of the lenses involved. Any change in these variables affects how much the microscope can magnify, helping to either bring minute details into clear view or leave them in obscurity.

Focal Length

Focal length is a critical concept in understanding how lenses work. It is the distance between the lens and the point where light rays meet to form a focused image. In microscopes, both the objective and eyepiece lenses have their own focal lengths, which play a crucial role in determining the magnifying power of the instrument.

• Objective Lens: The focal length of this lens (\(f_o\)) determines how much the specimen is initially magnified.
• Eyepiece Lens: Its focal length (\(f_e\)) further magnifies the image formed by the objective lens.

Shorter focal lengths can result in greater magnification but a smaller field of view, while longer focal lengths can provide less magnification but a wider field of view. In optical instruments such as microscopes, the focal length must be chosen carefully to strike a balance between magnification, clarity, and the practicality of viewing.