Ray Optics and Optical Instruments Previous Year Questions — JEE Main Physics
63 past-year Ray Optics and Optical Instruments questions from JEE Main (Physics) — page 4.
Q5 (2025)
A hemispherical vessel is completely filled with a liquid of refractive index $\mu$ . A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is
{{IMG1}}
- $\sqrt{3}$
- $\frac{3}{2}$
- $\sqrt{2}$
- $\frac{\sqrt{3}}{2}$
### Related Formula
$$\sin \mathrm{c} = \frac{1}{\mu}$$
### Core Logic
To see the coin from edge point $\mathrm{E}$ at grazing emergency, the light ray travelling from $mathrm{O}$ to $mathrm{E}$ must strike the flat upper boundary at the critical angle.
{{SOL_IMG1}}
Given the hemispherical layout geometry, the ray's angle of incidence at the center of the surface plane satisfies:
$$\theta = \mathrm{c} = 45^{\circ}$$
Substituting this value into the critical value expression:
$$\mu = \frac{1}{\sin 45^{\circ}} = \sqrt{2}$$
### Step 1: Final Conclusion
The minimum refractive index required is $\sqrt{2}$, matching option (3).
### Pattern Recognition
Grazing boundary ray vision configurations dictate evaluating the specific systemic geometric configuration to compute the critical boundary angle. Here, the radius profile fixes $\theta = 45^{\circ}$ deterministically.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Ray Optics and Optical Instruments
Q20 (2025)
A thin prism $\mathrm{P_1}$ with angle $4^{\circ}$ made of glass having refractive index 1.54, is combined with another thin prism $\mathrm{P_2}$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $\mathrm{P_2}$ in degrees is
- 4
- 3
- 16/3
- 1.5
### Related Formula
$$\delta = (\mu - 1)\mathrm{A}$$
### Core Logic
To achieve dispersion without deviation, the net deviation produced by the prism combination must be zero:
$$\delta_{\text{net}} = 0 \implies (\mu_1 - 1)\mathrm{A}_1 - (\mu_2 - 1)\mathrm{A}_2 = 0$$
Substituting the given parameters into the equation:
$$(1.54 - 1) \cdot 4^{\circ} - (1.72 - 1)\mathrm{A}_2 = 0$$
$$0.54 \cdot 4 = 0.72 \cdot \mathrm{A}_2$$
$$\mathrm{A}_2 = \frac{2.16}{0.72} = 3^{\circ}$$
### Step 1: Final Angle Value
The required angle for the second thin prism is $3^{\circ}$, which matches option (2).
### Pattern Recognition
For zero deviation conditions using thin components, balance the deviation equations directly: $(\mu-1)\mathrm{A} = (\mu'-1)\mathrm{A}'$.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Ray Optics and Optical Instruments
Q18 (2025)
The radii of curvature for a thin convex lens are $10\mathrm{~cm}$ and $15\mathrm{~cm}$ respectively. The focal length of the lens is $12\mathrm{~cm}$. The refractive index of the lens material is:
- $1.2$
- $1.4$
- $1.5$
- $1.8$
### Related Formula
Lens Maker's Formula:
$$\frac{1}{f} = (\mu - 1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$
where,
$f$ = focal length of the lens,
$\mu$ = refractive index of the material,
$R_1, R_2$ = radii of curvature with standard Cartesian sign convention.
### Core Logic
For a thin bi-convex lens, using standard coordinate conventions:
- $R_1 = +10\mathrm{~cm}$ (positive since first surface centers to the right of light trajectory),
- $R_2 = -15\mathrm{~cm}$ (negative since second surface centers to the left),
- Focal length $f = +12\mathrm{~cm}$.
### Step 1: Substituting in the Equation
Substitute the values into Lens Maker's formula:
$$\frac{1}{12} = (\mu - 1) \left(\frac{1}{10} - \frac{1}{-15}\right)$$
$$\frac{1}{12} = (\mu - 1) \left(\frac{1}{10} + \frac{1}{15}\right)$$
$$\frac{1}{12} = (\mu - 1) \left(\frac{3 + 2}{30}\right)$$
$$\frac{1}{12} = (\mu - 1) \left(\frac{5}{30}\right) = (\mu - 1) \left(\frac{1}{6}\right)$$
$$\mu - 1 = \frac{6}{12} = 0.5 \implies \mu = 1.5$$
### Pattern Recognition
Convex lenses always have opposite signs for $R_1$ and $R_2$. The term $\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ is additive: $\left(\frac{1}{|R_1|} + \frac{1}{|R_2|}\right)$.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Ray Optics and Optical Instruments
Q20 (2025)
Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below.
- A, C and D Only
- B, C and D Only
- A, B and E Only
- B, D and E Only
### Related Formula
For a prism of angle $A$:
- Deviation: $\delta = i + e - A$
- Minimum deviation $\delta_{\text{min}}$ occurs when:
$$i = e \quad \text{and} \quad r_1 = r_2 = \frac{A}{2}$$
- Under minimum deviation, the ray inside an equilateral/isosceles prism travels symmetrically, making it parallel to the prism base.
### Core Logic
Let's check the validity of each statement:
- **Statement (A)**: The refracted ray inside the prism becomes parallel to the base at minimum deviation. (True for symmetric prisms)
- **Statement (B)**: Larger angle prisms provide smaller minimum deviation. By minimum deviation equation:
$$\mu = \frac{\sin\left(\frac{A+\delta_{\text{min}}}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$
As $A$ increases, $\delta_{\text{min}}$ generally increases, not decreases. (False)
- **Statement (C)**: Angle of incidence $i$ and angle of emergence $e$ become equal ($i = e$) during the minimum deviation state. (True)
- **Statement (D)**: The $\delta-i$ curve is asymmetric and parabolic-like; for any deviation $\delta > \delta_{\text{min}}$, there are always exactly two different incident angles ($i$ and $e$) that yield the same deviation, except at the minimum deviation point (which has a single unique value). (True)
- **Statement (E)**: Angle of refraction $r = A/2$, which is half of the prism angle, not double. (False)
### Step 1: Conclusion
Since statements A, C, and D are true, the correct option is (1).
### Pattern Recognition
Review the classic parabolic shape of the deviation vs. angle of incidence ($\delta-i$) graph. Notice that any horizontal line above the minimum point intersects twice (representing $i$ and $e$ for that deviation). Minimum deviation is the unique local minimum, where $i = e$ and $r_1 = r_2 = A/2$.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Ray Optics and Optical Instruments: Refraction through Prism
Q19 (2025)
A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :
- 45 cm
- 7.5 cm
- 22.5 cm
- 15 cm
### Related Formula
Mirror Formula:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
### Core Logic
For the convex mirror, $u = -30\text{ cm}$ and $f = +30\text{ cm}$.
$$\frac{1}{v} - \frac{1}{30} = \frac{1}{30} \implies \frac{1}{v} = \frac{2}{30} \implies v = +15\text{ cm}$$
So, the convex mirror forms a virtual image 15 cm behind its surface.
### Step 1: Align Plane Mirror Image
The total distance from the object to the image location is $30 + 15 = 45\text{ cm}$.
For a plane mirror to create an image at this same exact location, it must be placed precisely midway between the object and the image.
Distance from object to plane mirror:
$$d = \frac{45}{2} = 22.5\text{ cm}$$
Therefore, the clearance distance between the convex mirror and the plane mirror surface is:
$$\text{Distance} = 30 - 22.5 = 7.5\text{ cm}$$
### Pattern Recognition
Coinciding images imply identical coordinate endpoints. Calculate the convex position explicitly, find the total path length from the real source object, and slice it in half for the plane mirror location.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Ray Optics and Optical Instruments
