Question

The magnifying power of objective of a compound microscope is \(5.0\) If the magnifying power of microscope is 30 , then magnifying power of eye-piece will be (A) 3 (B) 6 (C) 9 (D) 12

Short answer

The magnifying power of the eyepiece (M_ep) can be found using the formula: Magnifying Power (M) = Magnifying Power of Objective (M_obj) × Magnifying Power of Eyepiece (M_ep). Given the magnifying power of the microscope (M = 30) and the magnifying power of the objective lens (M_obj = 5.0), we can solve for M_ep: M_ep = 30 / 5.0, which gives M_ep = 6. The correct option is (B).

Step-by-step solution

The basic formula used to determine the magnifying power of a compound microscope is: Magnifying Power (M) = Magnifying Power of Objective (M_obj) × Magnifying Power of Eyepiece (M_ep) In this problem, we have M = 30 and M_obj = 5.0. We need to find the value of M_ep. #Step 2: Solve for M_ep#

Plug the given values into the formula and solve for M_ep: 30 = 5.0 × M_ep To isolate M_ep, divide both sides of the equation by 5.0: M_ep = 30 / 5.0 #Step 3: Calculate M_ep#

Perform the division: M_ep = 6 #Step 4: Match the answer with the options#

The calculated magnifying power of the eyepiece (M_ep) is 6. Compare this result with the given options: (A) 3 (B) 6 (C) 9 (D) 12 The correct option is (B).

Key concepts

Magnifying Power

The magnifying power of a compound microscope is a crucial concept. It signifies how much larger an object appears when viewed through the microscope compared to its actual size. This power is a cumulative effect of both the objective lens and the eyepiece lens. The formula to determine the overall magnifying power of a compound microscope is:\[ \text{Magnifying Power} (M) = \text{Magnifying Power of Objective} (M_{obj}) \times \text{Magnifying Power of Eyepiece} (M_{ep}) \]By understanding this formula, we can break down the contributions of each lens to the total magnification. It allows us to calculate the unknown magnifying power of either the objective or the eyepiece if we know the overall magnification and the power of the other lens. This is a vital calculation for accurately describing the capabilities of a microscope.

Objective Lens

The objective lens is one of the two main lenses in a compound microscope. It is located near the specimen being observed. The primary function of the objective lens is to gather light from the specimen and create an enlarged, inverted image that's real. This lens has a specific magnification, typically noted as M_obj. For example, in our exercise, the magnifying power of the objective lens is 5.0. - **High-power objectives:** These lenses have greater magnification, allowing them to view smaller details in a specimen. - **Low-power objectives:** These provide less magnification and a wider field of view, useful for larger specimens or when locating the area of interest on the slide. The choice of objective lens is crucial as it directly impacts the total magnification and the image quality that can be achieved.

Eyepiece Magnification

The eyepiece, or ocular lens, is the second key component that contributes to the magnifying power of a microscope. This lens is mounted on the side away from the specimen and is the part through which the viewer observes the enhanced image created by the objective lens. Its magnification is denoted as M_ep.In our example, we determined the eyepiece magnification by using the formula provided in the magnifying power section. Knowing the total magnifying power (30) and the power of the objective lens (5.0), we calculated:\[ M_{ep} = \frac{30}{5.0} = 6 \]This indicates that the eyepiece further enlarges the already magnified image produced by the objective lens, leading to a more detailed view of the specimen. The power of the eyepiece is crucial as it can be swapped to adjust the overall magnification of the microscope within a given range.

Optics

Optics, the study of light and lenses, is fundamental to understanding microscopes. These instruments rely on optical principles to magnify objects that are too small to be seen by the naked eye. Two primary lenses—the objective and the eyepiece—work together to bend light in such a way that a tiny subject appears much larger. Some essential concepts include:

• **Refraction**: The bending of light as it passes through lenses, which enables magnification.
• **Lens Shape**: Convex lenses are used because they converge light, allowing images to be magnified.
• **Resolution**: Beyond simple magnification, optics also influence the clarity and detail of the image, known as resolution. Higher resolution gives finer details.

Understanding optics empowers users to make informed choices about microscope settings and lens combinations to achieve the desired level of detail in their observations.