Consider the following statements : 1. The focal length of the objective of a microscope is less than the focal length of the eyepiece. 2. The minimum distance between an object and its real image formed by a convex lens of focal length f is equal to 4 f. Which of the statements given above is/are correct?

Statement 1 is correct because in a compound microscope, the objective lens must have a very short focal length (typically 10mm or less) to produce high initial magnification of the small object [t1][t8]. The eyepiece, while also having a short focal length, generally has a focal length greater than that of the objective to comfortably magnify the intermediate real image [t1][t8]. Statement 2 is correct based on the thin lens formula (1/f = 1/v + 1/u). For a convex lens to form a real image, the distance between the object and the image (D = u + v) is minimized when u = v = 2f. At this symmetric point, the object and image are both at 2f from the lens, making the total distance D = 2f + 2f = 4f [c3][t2]. Any other configuration results in a distance greater than 4f.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > QUESTIONS > p. 158