Understanding Microscope Optics

To determine the correct statements about optical microscopes, let's analyze each statement individually:

Statement Analysis

• Statement 1: Both the eyepiece and objective of a microscope are convex lenses.

  This statement is correct. In a compound microscope, the objective lens gathers light from the specimen and forms a magnified real image. The eyepiece lens then acts like a magnifying glass to view this intermediate image, producing a final virtual image. Both lenses function as converging lenses, which are convex.

• Statement 2: The magnification of a microscope increases with increase in focal length of the objective.

  This statement is incorrect. The magnification of the objective lens ($M_o$) is related to the tube length ($L$) and the objective's focal length ($f_o$) by the approximate formula $M_o \approx L/f_o$. Therefore, magnification decreases as the focal length of the objective increases.

• Statement 3: The magnification of a microscope depends upon the length of the microscope tube.

  This statement is correct. As seen in the formula $M_o \approx L/f_o$, the magnification contributed by the objective lens is directly proportional to the tube length ($L$). A longer tube allows for greater magnification, assuming other factors remain constant.

• Statement 4: The eyepiece of a microscope is a concave lens.

  This statement is incorrect. As explained in the analysis of Statement 1, the eyepiece of a standard optical microscope is a convex lens, used to magnify the intermediate image formed by the objective.

Conclusion

Based on the analysis, statements 1 and 3 are correct, while statements 2 and 4 are incorrect.

Therefore, the correct option is the one that includes statements 1 and 3.