Railway Science (Physics-Light and Optics) (Part-VI)

Total Questions: 50

41. A 1.0-cm long object is placed at a distance of 12 cm on the principal axis of a convex lens of focal length 8 cm. The height of the image formed will be ________. [RRC Group D 26/08/2022 (Afternoon)]

Correct Answer: (a) 2.0 cm
Solution:

2.0 cm. Here, u = - 12 cm , f = 8 cm, height of object = 1 cm.
According to lens formula

42. The radius of curvature of a convex mirror is 15 cm. Following the New Cartesian sign Convention, the principal focus is located at x = ? [RRC Group D 29/08/2022 (Morning)]

Correct Answer: (a) 7.5 cm
Solution:

7.5 cm. The sign is taken as negative in front of a spherical mirror. Sign is taken as positive behind the spherical mirror. Since, the center of curvature and focus lies behind the convex mirror, so radius of curvature and focal length are taken as positive in the case of convex mirror.
Hence, R = 15 cm
Now, f = R / 2 = 15 / 2 = 7.5 cm

43. An object is placed in front of a concave mirror of focal length 15 cm and its image is formed on the same side as the object, at a distance of 45 cm. The distance of the object from the mirror is: [RRC Group D 29/08/2022 (Evening)]

Correct Answer: (c) 22.5 cm
Solution:

22.5 cm. Since, the object is always placed in front of the mirror hence the sign of the object is taken as negative. Since, the center of curvature and focus lie in front of the concave mirror, signs of the radius of curvature and focal length are taken as negative in the case of the concave mirror.
Given, f = -15 cm and v = - 45 cm.
then u = distance of the object from the mirror.

44. The refractive indices of ice and glass are 1.31 and 1.52, respectively. A ray of light passes from ice to glass. The refractive index of glass with respect to ice is ______ and the ray bends _______ the normal in glass. [RRC Group D 30/08/2022 (Morning)]

Correct Answer: (c) 1.16, towards
Solution:


refractive index of material 2 w.r.t.
Material 1. So, the refractive index of
glass with respect to ice is = 1.52/1.31 =
1.16. When a light ray travels from a rarer
medium to a denser medium, the speed
of light reduces, and it bends towards the
normal. Here, ice is rare medium and
glass is denser. So, the ray will bend
towards the normal.

45. The radius of curvature of a concave mirror is 12 cm. Following the New Cartesian Sign Convention, the principal focus is located at x = ___________. [RRC Group D 30/08/2022 (Morning)]

Correct Answer: (c) -6 cm
Solution:

-6 cm. Since, the center of curvature and focus lie in front of the concave mirror, signs of the radius of curvature and focal length are taken as negative in the case of the concave mirror. Here, R = -12 cm. So, f = R / 2 = -12/2 = -6 cm.

46. The focal length of a concave mirror is 24 cm. Following New Cartesian Sign Convention, its center of curvature is located at: [RRC Group D 30/08/2022 (Afternoon)]

Correct Answer: (a) -48 cm
Solution:

- 48 cm. The sign is always taken as negative in front of a concave mirror. Since, the center of curvature and focus lie in front of the concave mirror, signs of the radius of curvature and focal length are taken as negative. Here, f = - 24 cm. So, R = 2f = - 48 cm.

47. An object is placed on the principal axis of a lens of power -10 D, at a distance of 15 cm. The image formed is _______. [RRC Group D 30/08/2022 (Evening)]

Correct Answer: (c) virtual and erect
Solution:

Virtual and erect.
Given, Power = -10 D,
Distance of object (u) = - 15 cm.
Now,
Focal length, f = 1/𝑃.
= 1/10 = - 0.1 m = -10 cm.
Because the focal length is negative, the given lens is concave lens and in the case of concave lens no matter where the object is placed other than infinity, the virtual and Erect image will be formed between the optical center and the focus of the concave lens.

48. The focal length of a convex mirror is 15 cm. Following New Cartesian Sign Convention, its center of curvature is located at: [RRC Group D 30/08/2022 (Evening)]

Correct Answer: (a) 30 cm
Solution:

30 cm. Center of curvature is situated at 2f. Hence, C = 2f = 2(15) = 30 cm. According to the new cartesian sign Convention the center of curvature and focus lies behind in the convex mirror, so signs of the radius of curvature and focal length are taken as + (positive) in this case.

49. According to mirror formula, the focal length of a spherical mirror is equal to: [RRC Group D 01/09/2022 (Morning)]

Correct Answer: (d)
Solution:

50. A converging lens having focal length 50 cm is kept in contact with a diverging lens having focal length 20 cm. The power of combination of the two lenses is: [RRC Group D 01/09/2022 (Morning)]

Correct Answer: (d) - 3 D
Solution:

- 3 D. For converging lenses, the focal length is always positive, while diverging lenses always have negative focal lengths. Therefore, f₁ = 50 cm and f₂ = - 20 cm.