Question

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: For a simple microscope, the angular size of the object equals the angular size of the image.

Reason R: Magnification is achieved as the small object can be kept much closer to the eye than $25cm$ and hence it subtends at a large angle.

In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both A and R are true but R is NOT the correct explanation of A
• B. Both A and R are true and R is the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is B

Both A and R are true and R is the correct explanation of A

The explanation for the Assertion statement:

Magnification in microscope

Microscopes have a Convex lens for the magnification of objects.

From the diagram, for image and object, the angle subtended is the same, that is the angular size of the image and object is the same.

${\theta }_o={\theta }_i$

Hence the angular size of the image and object is the same.

The explanation for Reason statement:

Since ${\theta }_o={\theta }_i$, we have

$\Rightarrow \frac{h_o}{u_o}=\frac{h_i}{D}$

where $h_o$ is height of object and $h_i$ is height of image

and, $u_o$ is distance of object from lens and $D$ is distance of image from lens

If the object is kept very close to the lens, the angle subtended will be large, implying that a large image will be formed, hence magnification is achieved. This can be also shown by considering the angular size of the image and object.

Hence, option B is correct.