Question

In a compound microscope (1) the objective has a shorter focal length (2) the objective has a shorter aperture (3) \((1)\) and \((2)\) both are correct (4) the aperture of objective and eyepiece are same.

Short answer

Both statement (1) and (2) are correct. The correct answer is (3).

Step-by-step solution

- Understand the Microscope Parts

A compound microscope consists of an objective lens and an eyepiece lens. The objective lens is the one closest to the specimen, and the eyepiece is the one through which you look.

- Examine the Options

Look at the given statements to determine their correctness: (1) the objective has a shorter focal length, (2) the objective has a shorter aperture, (3) (1) and (2) both are correct, (4) the aperture of objective and eyepiece are same.

- Analyze Focal Length

The objective lens of a compound microscope indeed has a shorter focal length. This is necessary to increase the magnification of the specimen.

- Analyze Aperture

The objective lens also typically has a shorter aperture compared to the eyepiece. A smaller aperture in the objective allows for better resolution and depth of field in microscopy.

- Validate Mixed Statements

Since both statement (1) and statement (2) are true, statement (3) must also be true.

- Invalidate Same Aperture

The aperture size of the objective and eyepiece are not the same, thus statement (4) is incorrect.

Key concepts

Objective Lens

The objective lens in a compound microscope is crucial because it is the one closest to the specimen. Its main role involves gathering light from the sample and creating a magnified image.
One key characteristic of the objective lens is having a shorter focal length. This helps increase the magnification, allowing us to see fine details. The objective lens must be designed meticulously as it affects the overall performance of the microscope.
There are usually different objective lenses available on a microscope, each offering different magnification levels, such as 4x, 10x, 40x, and 100x.

Focal Length

Focal length is a critical concept in microscopy. It refers to the distance between the lens and the point where it focuses light.
In a compound microscope, the objective lens has a very short focal length. This allows it to create a highly magnified image of the specimen.
Shorter focal lengths lead to higher magnification because the lens bends light rays more sharply. This is vital for examining microscopic details that are not visible to the naked eye. By using a lens with a shorter focal length, researchers can achieve greater clarity and detail in their samples.

Aperture in Microscopy

Aperture in microscopy refers to the diameter of the lens through which light enters. This plays a significant role in determining the resolution and depth of field.
The objective lens typically has a smaller aperture compared to the eyepiece. A smaller aperture in the objective helps in achieving better resolution, meaning you can see finer details more clearly.
Moreover, it improves the depth of field, which is the thickness of the specimen that can be in focus at one time. In summary, understanding aperture is essential for making the best use of a microscope's capabilities.