Question

Draw a ray diagram to show the image formation by a compound microscope. Obtain the expression for the total magnification of the microscope when the final image is formed at infinity.

Answer 1

Compound Microscope:

A compound microscope consists of two lenses: the objective lens and the eyepiece. The objective lens forms a real, inverted, and magnified image of the object, and the eyepiece magnifies this image further.

- The object is placed slightly inside the focal point of the objective lens.

- The objective lens produces a real, inverted, and magnified image, which acts as the object for the eyepiece.

- The eyepiece forms an image at infinity, as the final image is formed at infinity (in a relaxed eye condition).

Total Magnification:

The total magnification \( M_{\text{total}} \) of the microscope is the product of the magnification produced by the objective lens \( M_{\text{obj}} \) and the magnification produced by the eyepiece \( M_{\text{eyepiece}} \):

\[ M_{\text{total}} = M_{\text{obj}} \times M_{\text{eyepiece}} \]

1. Objective Magnification:

The magnification of the objective lens is given by:

\[ M_{\text{obj}} = - \frac{v_{\text{obj}}}{u_{\text{obj}}} \]

Where \( v_{\text{obj}} \) is the image distance and \( u_{\text{obj}} \) is the object distance for the objective lens.

2. Eyepiece Magnification:

The magnification of the eyepiece is given by:

\[ M_{\text{eyepiece}} = \frac{D}{f_{\text{eyepiece}}} \]

Where \( D \) is the near point distance of the eye (usually taken as 25 cm), and \( f_{\text{eyepiece}} \) is the focal length of the eyepiece.

Thus, the total magnification is the product of these two magnifications.