Find the maximum magnifying power of a compound microscope having a 25d lens as the objective ,a 5d lens as the eyepiece and the sepration 30cm between the two lenses .The least distance for a clear vision is 25cm

To determine the maximum magnifying power of a compound microscope, we need to consider the characteristics of both the objective and the eyepiece lenses, as well as their arrangement. The magnifying power (M) of a compound microscope can be calculated using the formula:

Understanding the Components

In this case, we have:

• Objective lens focal length (f_o) = 25d
• Eyepiece lens focal length (f_e) = 5d
• Separation between the lenses (d) = 30 cm
• Least distance of distinct vision (D) = 25 cm

Calculating the Magnifying Power

The total magnifying power of the microscope can be expressed as:

M = M_o × M_e

Where:

• M_o = Magnifying power of the objective lens
• M_e = Magnifying power of the eyepiece lens

Step 1: Magnifying Power of the Objective Lens

The magnifying power of the objective lens can be calculated using the formula:

M_o = \frac{v}{u} = \frac{D}{f_o - d}

Here, v is the image distance, u is the object distance, and d is the distance between the lenses. For the objective lens, we can assume that the object is placed at its focal point, so:

u = f_o = 25d

Substituting the values:

M_o = \frac{D}{f_o - d} = \frac{25}{25 - 30} = \frac{25}{-5} = -5

The negative sign indicates that the image is inverted, which is typical for objective lenses.

Step 2: Magnifying Power of the Eyepiece Lens

The magnifying power of the eyepiece lens is given by:

M_e = 1 + \frac{D}{f_e}

Substituting the values:

M_e = 1 + \frac{25}{5} = 1 + 5 = 6

Final Calculation of Total Magnifying Power

Now, we can find the total magnifying power:

M = M_o × M_e = (-5) × 6 = -30

The negative sign indicates that the final image is inverted, which is a common characteristic of compound microscopes.

Conclusion

The maximum magnifying power of the compound microscope, given the specified parameters, is 30 times. This means that the image produced by the microscope is 30 times larger than the actual object being viewed. Understanding these calculations helps in appreciating how microscopes enhance our ability to observe minute details in various fields, from biology to materials science.