STD 12 - Ray optics and optical instruments PYQs: JEE Mains Physics

Showing 1–50 of 248 questions

1. 1. A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be :
   2026 Easy
2. 2. A collimated beam of light of diameter 2 mm is propagating along x -axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm , then the focal length of second lens is _________ mm. 2026 Medium
3. 3. A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be 2026 Hard
4. 4. A concave mirror of focal length \(10\) cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is __________ cm. 2026 Medium
5. 5. A convex lens is made from glass material having refractive index of \(1.4\) with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______. 2026 Medium
6. 6. A convex lens of refractive index 1.5 and focal length \(f=18 cm\) is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is \(\alpha \times f\). The value of \(\alpha\) is ___________.
   (refractive index of water \(=4 / 3\) ) 2026 Medium
7. 7. A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm . Refractive index of glass is 1.5 . The rays converge to a point at a distance x cm from the centre of the curvature of the spherical surface. The value of x is __________ cm. 2026 Medium
8. 8. A prism of angle \(75^{\circ}\) and refractive index \(\sqrt{3}\) is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ___________ .
   \(\left(\sin 15^{\circ}=0.25\right.\) and \(\left.\sin 25^{\circ}=0.43\right)\) 2026 Easy
9. 9. A ray of light passing through an equilateral prism is having velocity \(2.12 \times 10^8\) m/s in the prism material, then the minimum angle of deviation is _________ degrees. 2026 Medium
10. 10. A rod of length \(10\) cm lies along the principle axis of a concave mirror of focal length \(10\) cm as shown in figure. The length of the image is _____ cm.
    2026 Medium
11. 11. A spherical interface lens of radius \(R\) separates two media of refractive indices \(1\) and \(1.4\) respectively as shown in the figure below. A point source is placed at a distance of \(4R\) in front of spherical interface. The magnitude of the magnification of point source image is _______.
    2026 Medium
12. 12. A thin biconvex lens is prepared from the glass (\(\mu=1.5\)) both curved surfaces of which have equal radii of \(20\) cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm. 2026 Hard
13. 13. A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ? 2026 Medium
14. 14. A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification \( m_{1} \), when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to \( m_{2} \).
    The value of \(\left|\frac{m_1}{m_2}\right|\) is __________ . 2026 Medium
15. 15. A thin prism with angle \( 5^{\circ} \) of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is ___________. 2026 Medium
16. 16. An object \(AB\) is placed \(15\text{ cm}\) on the left of a convex lens \(P\) of focal length \(10\text{ cm}\). Another convex lens \(Q\) is now placed \(15\text{ cm}\) right of lens \(P\). If the focal length of lens \(Q\) is \(15\text{ cm}\), the final image is _______. 2026 Medium
17. 17. Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________. 2026 Medium
18. 18. As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.
    
    If refractive index of the material of prism is \(\sqrt{2}\), the angle \(\theta\) of prism is. 2026 Medium
19. 19. Consider an equilateral prism (refractive index \( \sqrt{2} \)). A ray of light is incident on its one surface at a certain angle i. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to __________ . 2026 Hard
20. 20. Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media \(A\) and \(B\) are \(2.4 \times 10^8 m / s\) and \(2.7 \times 10^8 m / s\) respectively, then the value of critical angle is : 2026 Hard
21. 21. Distance between an object and three times magnified real image is 40 cm . The focal length of the mirror used is _________ cm . 2026 Medium
22. 22. Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (u) and image distance (v) using same convex lens having power +5 D as \((25,96),(30,62)\), \((35,37),(45,35)\) and \((50,32)\) respectively. Identify correct statement 2026 Hard
23. 23. For a thin symmetric prism made of glass (refractive index \(1.5\)), the ratio of incident angle and minimum deviation will be _______. 2026 Medium
24. 24. For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies. 2026 Easy
25. 25. If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at \(30\) cm above the paper. If the radius of curvature of the lens is \(60\) cm then the refractive index of the lens material is \(\dfrac{\alpha}{10}\). The value of \(\alpha\) is _______. 2026 Medium
26. 26. In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm . Total magnification obtained with this system for normal adjustment is \((5)^{ k }\). The value of k is _________ 2026 Easy
27. 27. In a microscope the objective is having focal length \(f_0=2 cm\) and eye-piece is having focal length \(f_{ e }=4 cm\). The tube length is 32 cm . The magnification produced by this microscope for normal adjustment is _________ . 2026 Hard
28. 28. In parallax method for the determination of focal length of a concave mirror, the object should always be placed : 2026 Easy
29. 29. Light ray incident along a vector \(\vec{AO}\) \((\vec{AO} = 2\hat{i}-3\hat{j})\) emerges out along vector \(\vec{OB}\) \((\vec{OB} = C\hat{i}-4\hat{j})\) as shown in the figure below. The value of \(C\) is ________.
    2026 Hard
30. 30. One side of an equilateral prism is painted by a transparent material of refractive index \(n_2\). The refractive index of prism is \(1.6\). The minimum value of \(n_2\) required for total internal reflection from painted face is _______.
    2026 Hard
31. 31. Refer the figure given below. \(\mu_1\) and \(\mu_2\) are refractive indices of air and lens material. The height of image will be _______ cm.
    2026 Medium
32. 32. The exit surface of a prism with refractive index \(n\) is coated with a material having refractive index \(\frac{ n }{2}\). When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is _________ 2026 Medium
33. 33. The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index \(=1.7\)) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ___________ . 2026 Easy
34. 34. The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ___________ cm. 2026 Medium
35. 35. The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is \(\frac{4}{3}\).The wavelength of the same light when it is passing through a transparent medium having refractive index of \(\frac{3}{2}\) is __________ nm. 2026 Easy
36. 36. A bi-convex lens has radius of curvature of both the surfaces same as \(1 / 6 \mathrm{~cm}\). If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides \(\left(R_1 \neq R_2\right)\), without any change in lens power then possible combination of \(R_1\) and \(R_2\) is : 2025 Hard
37. 37. A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm , respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be _______. 2025 Hard
38. 38. A concave mirror of focal length \(f\) in air is dipped in a liquid of refractive index \(\mu\). Its focal length in the liquid will be: 2025 Medium
39. 39. A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is : 2025 Easy
40. 40. A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is ______ cm.
    (Consider liquids are immisible) 2025 Medium
41. 41. A convex lens made of glass (refractive index \(=1.5\) ) has focal length 24 cm in air. When it is totally immersed in water (refractive index \(=1.33\) ), its focal length changes to ________. 2025 Medium
42. 42. A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is ________ 2025 Easy
43. 43. 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 : 2025 Medium
44. 44. A hemispherical vessel is completely filled with a liquid of refractive index \(\mu\). A small coin is kept at the lowest point \((\mathrm{O})\) 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 _______.
    2025 Hard
45. 45. A lens having refractive index 1.6 has focal length of 12 cm , when it is in air. Find the focal length of the lens when it is placed in water.
    (Take refractive index of water as 1.28) 2025 Easy
46. 46. A mirror is used to produce an image with magnification of \(\frac{1}{4}\). If the distance between object and its image is 40 cm , then the focal length of the mirror is ________ 2025 Hard
47. 47. A monochromatic light of frequency \(5 \times 10^{14} \mathrm{~Hz}\) travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be : 2025 Easy
48. 48. A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is \(2 \mathrm{~cm} \times 2 \mathrm{~cm}\) and the area of the landscape photographed is \(400 \mathrm{~km}^2\). The focal length of the lens in the drone camera is : 2025 Easy
49. 49. A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of \(f_1\) in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of \(\mathrm{f}_2\) when it is immersed in a liquid of refractive index 1.2 . If both the lenses are made of same glass of refractive index 1.5 , the ratio of \(f_1\) and \(f_2\) will be _______. 2025 Hard
50. 50. A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to \(60^{\circ}\). The refractive index of the prism material is \(\sqrt{2}\). The angle of incidence (in degrees) is ______. 2025 Easy

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