Question

For a microscope to work as intended, the separation between the objective lens and the eyepiece must be such that the intermediate image produced by the objective lens will occur at a distance (as measured from the optical center of the eyepiece) a) slightly larger than the focal length. b) slightly smaller than the focal length. c) equal to the focal length. d) The position of the intermediate image is irrelevant.

Short answer

Question: In order for the eyepiece lens of a compound microscope to further magnify the intermediate image produced by the objective lens, the intermediate image must be formed at a distance from the eyepiece lens that is: a) equal to the focal length b) slightly smaller than the focal length c) slightly larger than the focal length d) much larger than the focal length Answer: b) slightly smaller than the focal length.

Step-by-step solution

Understand the basic structure of a compound microscope

A compound microscope consists of two convex lenses: the objective lens and the eyepiece lens. The objective lens has a smaller focal length than the eyepiece lens. The specimen is placed close to the focus of the objective lens. The objective lens forms a magnified, inverted real image, also known as the intermediate image, of the specimen which is further magnified by the eyepiece lens to form the final image perceived by the observer.

Understand the placement of intermediate image with respect to the eyepiece lens

The intermediate image formed by the objective lens needs to be in focus when viewed through the eyepiece lens. For this to happen, the intermediate image should be placed within the focal length of the eyepiece lens. This will ensure that the rays diverging from the intermediate image enter the eyepiece lens and converge at a point within or near the user's eye to form a magnified, inverted virtual image of the intermediate image.

Comparing the focal length of the eyepiece with the distance requirement for the intermediate image

In order for the eyepiece lens to further magnify the intermediate image, the intermediate image must be formed within the focal length of the eyepiece lens. If the intermediate image is formed exactly at the focal point, the eyepiece lens would only convert the diverging rays to parallel rays and magnification would be limited. Therefore, the ideal distance of the intermediate image is slightly less than the focal length of the eyepiece lens.

Selecting the correct answer

Based on the understanding of the placement of the intermediate image with respect to the eyepiece lens, we can conclude that the correct answer is: b) slightly smaller than the focal length.