(a) Speed of light in glass is 2 × 10^8 m/s. Refractive index of glass is ______. (Score : 1)
(b) For an equilateral prism made of a material of refractive index √2, find the angle of minimum deviation for a ray of monochromatic light. (Scores : 2)
(c) Draw the ray diagram of a s

Question

(a) Speed of light in glass is 2 × 10^8 m/s. Refractive index of glass is ______. (Score : 1)
(b) For an equilateral prism made of a material of refractive index √2, find the angle of minimum deviation for a ray of monochromatic light. (Scores : 2)
(c) Draw the ray diagram of a simple microscope that uses a single convex lens. Derive an expression for its linear magnification. (Scores : 3)

Accepted Answer

![Figure — Part (c) explicitly says 'Draw the ray diagram of a simple microscope that uses a single convex lens' (3 marks](/figures/ray-optics-and-optical-instruments/simple-microscope-magnifying-lens-located-image-near-fig-9-23.svg)

>

> [!TLDR]
> (a) n = c/v = 1.5. (b) For an equilateral prism (A=60°) with n=√2, the minimum-deviation formula gives Dm = 30°. (c) A simple microscope is a single convex lens with the object inside its focal length; its angular magnification is m = 1 + D/f.
>
> **(a) Refractive index of glass**
>
> $$n = \frac{c}{v} = \frac{3	imes10^{8}}{2	imes10^{8}} = 1.5$$
>
> **(b) Angle of minimum deviation for an equilateral prism**
>
> For an equilateral prism the prism angle $A = 60°$. The prism formula relating refractive index n, prism angle A and the angle of minimum deviation $D_m$ is
>
> $$n = \frac{\sin\left(\dfrac{A+D_m}{2}ight)}{\sin\left(\dfrac{A}{2}ight)}$$
>
> Given $n=\sqrt{2}$ and $A=60°$, so $A/2 = 30°$, $\sin 30° = 0.5$:
>
> $$\sqrt{2} = \frac{\sin\left(\dfrac{60+D_m}{2}ight)}{0.5} \implies \sin\left(\frac{60+D_m}{2}ight) = 0.5\sqrt{2} = \frac{\sqrt2}{2} = \sin45°$$
>
> $$\frac{60+D_m}{2} = 45° \implies 60+D_m = 90° \implies D_m = 30°$$
>
> **(c) Simple microscope — ray diagram and magnification**
>
> A simple microscope is just a single convex (converging) lens of short focal length, used to view small objects by placing them within the focal length of the lens, so the lens forms a virtual, erect, magnified image.
>
> *Ray diagram (described):* The object O is placed between the lens's optical centre and its focus F (i.e. at a distance $u < f$). Two rays are drawn from the top of the object: one travels parallel to the principal axis and, after refraction, appears to come from the focus F on the object's side; the other passes straight through the optical centre undeviated. Both refracted rays diverge on the object's side of the lens, and tracing them backward (with dashed lines), they appear to meet at a point behin

Q.(a) Speed of light in glass is 2 × 10^8 m/s. Refractive index of glass is ______. (Score : 1)

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.(a) Speed of light in glass is 2 × 10^8 m/s. Refractive index of glass is ______. (Score : 1)

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