With the help of ray diagram, describe the construction, working of a compound microscope when the final image is formed at least distance of distinct vision (D = 25cm). Derive an expression for its magnifying power (m).

**OR**

(a) Two lenses of powers +15D and –5D are in conta

Question

With the help of ray diagram, describe the construction, working of a compound microscope when the final image is formed at least distance of distinct vision (D = 25cm). Derive an expression for its magnifying power (m).

**OR**

(a) Two lenses of powers +15D and –5D are in contact with each other. What is the focal length of combination ?
(b) In the Young's double slit experiment, two slits 0.125mm apart are illuminated by light of wavelength 4500A°. The screen is 1m away from the plane of the slits. Find the separation between second bright fringes on both sides of central maxima.

Accepted Answer

![Figure — Answer takes the compound-microscope alternative with final image at the near point D; NCERT fig 9.24 is the r](/figures/ray-optics-and-optical-instruments/ray-formation-image-compound-microscope-fig-9-24.svg) > > [!TLDR] > The objective forms a real, magnified, inverted image just inside the eyepiece's focal length; the eyepiece then acts as a simple magnifier on that image, giving overall magnifying power $m\approx \dfrac{L}{f_o}\cdot\dfrac{D}{f_e}$ when the final image is at the near point. > > **Construction:** A compound microscope has two convex lenses mounted coaxially at the two ends of a tube: the OBJECTIVE (facing the object), of small aperture and small focal length $f_o$, and the EYEPIECE (near the eye), of slightly larger focal length $f_e$, separated by a distance $L$ (the tube length). > > **Working / ray diagram (described):** The object O is placed just beyond the objective's focus ($f_o < u_o < 2f_o$), so the objective forms a real, inverted, magnified image $I_1$ a little inside the focal length of the eyepiece. This intermediate image $I_1$ then acts as the 'object' for the eyepiece, which — since $I_1$ lies within the eyepiece's focal length — forms a further magnified, VIRTUAL image $I_2$ that the eye sees. If $I_2$ is formed at the near point (least distance of distinct vision, $D=25$ cm), the eyepiece is essentially working as a simple magnifier in its maximum-magnification configuration. > > **Magnifying power derivation:** Overall magnification is the product of the objective's linear magnification and the eyepiece's angular magnification: …

Q.With the help of ray diagram, describe the construction, working of a compound microscope when the final image is formed at least distance of distinct vision (D = 25cm). Derive an expression for its magnifying power (m). OR

Concept understanding — Microscope Magnification

Microscope Magnification

How the two lenses work together

The objective's magnification

The eyepiece's magnification

Total magnifying power

Worked example

Why this formula?

Microscope Magnification: Why the Formula Holds

1. What Does "Magnification" Mean in a Microscope?

2. The Key Formula

3. Derivation of Objective Magnification $M_o$

Step 1: How the objective works

Step 2: Using the lens formula

Step 3: The tube length approximation

Step 4: Magnification formula

4. Derivation of Eyepiece Magnification $M_e$

Step 1: The eyepiece as a simple magnifier

Step 2: Angular magnification

Q.With the help of ray diagram, describe the construction, working of a compound microscope when the final image is formed at least distance of distinct vision (D = 25cm). Derive an expression for its magnifying power (m). OR

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