The focal length of the objective of a compound microscope is \( f_o \) and its distance from the eyepiece is L. An object is placed at a distance u from the objective. For proper working of the instrument
(A) \( L \lt u \)
(B) \( L \gt u \)
(C) \( f_o \lt L \lt 2f_o \)
(D) \( L \gt 2f_o \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (D) only
In a compound microscope the object is placed just outside the focus of the objective, so \( f_o \lt u \lt 2f_o \). The objective then forms a real, magnified image at a distance \( v \gt 2f_o \) on the other side. The eyepiece is placed beyond this image, so the distance between the lenses satisfies \( L \gt v \).
Since \( v \gt 2f_o \gt u \), it follows that \( L \gt v \gt u \) and \( L \gt v \gt 2f_o \).
(A) \( L \lt u \) — Incorrect. The eyepiece is farther from the objective than the object is.
(B) \( L \gt u \) — Correct. \( L \gt v \gt u \).
(C) \( f_o \lt L \lt 2f_o \) — Incorrect. The image itself is already beyond \( 2f_o \), so \( L \) cannot be less than \( 2f_o \).
(D) \( L \gt 2f_o \) — Correct. \( L \gt v \gt 2f_o \).
Statements (B) and (D) are correct, which is Option (2).