Question

Draw the labelled ray diagram for the formation of image by a compound microscope. Derive the expression for the total magnification of a compound micro-scope. Explain why both the objective and the eyepiece of a compound microscope must have short focal lengths.

Answer 1

It is an instrument used to see highly magnified image of tiny objects.

Principle: It is based on the principle that when a small object is placed just outside the focus of objective lens, its real, inverted and magnified image is formed on the other side of the lens. This image acts as an object for eye lens, the eye lens is so adjusted that the final image is produced at least distance of distinct vision.

Construction: It consists of two convex lenses of shorter focal lengths arranged co-axially at the ends of two sliding tubes.

(i) Objective: It is a convex lens of very short focal length and of small aperture and is placed near the object to be magnified.

(ii) Eye piece: It is a convex lens of short focal length and of comparatively large aperture and is placed near the eye for seeing the final image which is formed at least distance of distinct vision.

The distance between the two lenses can be adjusted by rack and pinion arrangement.

Let a tiny object AB be placed in front of objective at a distance more than f₀. Its real and enlarged image is formed at A' B'. This image A'B' acts as an object for eye piece and forms final image at A"B" i.e. at a distance D, the distance of distinct vision.

Magnifying Power of Microscope is defined as the ratio of the angle subtended on the eye by the final image to the angle subtended on the eye by the object, when both the final image and the object are situated at least distance of distinct vision.

Magnifying power, M = \(\frac{\beta}{\alpha}\)

Since angles are small, therefore, tan ß ≃ ß and tan α ≃ α.

(Negative sign shows that final image is inverted with respect to the object.)

Thus we find that, if the focal length of objective lens and eye lens are short, the magnifying power will be large. Magnifying power of compound microscope when final image is at infinity. Magnifying power is defined as the angle subtended on the eye by the final image to the angle subtanded on the eye by the object, at the unaided eye, when final image is formed at infinity. When final image is formed at infinity.

The angular magnification due to eye piece m_e = \(\frac{D}{f_e}\)

The angular magnification due to objective lens m₀ = \(\frac{L}{f_0}\)

∴ M = m₀m_e = \(\frac{L}{f_0} \times \frac{D}{f_e}\)

Thus we find that, to have large magnification, the focal length of the objective lens and eye lens must be small.