Optics
Q. A double convex lens has a focal length of 10 cm. If it is made of a material with a refractive index of 1.5, what is the radius of curvature of each surface assuming they are equal?
A.
15 cm
B.
20 cm
C.
25 cm
D.
30 cm
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Solution
Using the lens maker's formula, R = 2f(n-1) = 2*10*(1.5-1) = 20 cm.
Correct Answer: B — 20 cm
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Q. A double convex lens has a radius of curvature of 20 cm on both sides. What is its focal length if the refractive index is 1.5?
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Using the lens maker's formula, f = R/(n-1), we find f = 20/(1.5-1) = 40 cm.
Correct Answer: A — 10 cm
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Q. A fiber optic cable uses total internal reflection to transmit light. What is the primary requirement for this to work effectively?
A.
The core must have a higher refractive index than the cladding
B.
The cladding must have a higher refractive index than the core
C.
The light must be monochromatic
D.
The cable must be straight
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Solution
For total internal reflection to occur in a fiber optic cable, the core must have a higher refractive index than the cladding.
Correct Answer: A — The core must have a higher refractive index than the cladding
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Q. A fiber optic cable uses total internal reflection. If the refractive index of the core is 1.5 and that of the cladding is 1.4, what is the critical angle?
A.
42.0°
B.
48.6°
C.
60.0°
D.
30.0°
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Solution
Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.4/1.5) ≈ 42.0°.
Correct Answer: A — 42.0°
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Q. A fiber optic cable uses total internal reflection. If the refractive index of the core is 1.6 and the cladding is 1.5, what is the critical angle?
A.
38.7°
B.
41.8°
C.
48.6°
D.
60.0°
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Solution
Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.5/1.6) ≈ 38.7°.
Correct Answer: A — 38.7°
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Q. A fiber optic cable uses total internal reflection. What is the minimum refractive index required for the core if the cladding has a refractive index of 1.45?
A.
1.50
B.
1.45
C.
1.60
D.
1.75
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Solution
For total internal reflection, the core must have a higher refractive index than the cladding, so it must be greater than 1.45.
Correct Answer: A — 1.50
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Q. A fiber optic cable uses total internal reflection. What is the role of the cladding?
A.
To increase the refractive index.
B.
To decrease the refractive index.
C.
To prevent light loss.
D.
To enhance light absorption.
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Solution
The cladding has a lower refractive index than the core, ensuring that light is kept within the core through total internal reflection.
Correct Answer: C — To prevent light loss.
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Q. A fiber optic cable uses total internal reflection. What is the role of the cladding in this context?
A.
To increase the speed of light.
B.
To provide structural support.
C.
To ensure light remains within the core.
D.
To change the wavelength of light.
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Solution
The cladding has a lower refractive index than the core, ensuring that light remains within the core by total internal reflection.
Correct Answer: C — To ensure light remains within the core.
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Q. A lens forms a real image at a distance of 30 cm from the lens when the object is placed at 10 cm. What is the focal length of the lens?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Using the lens formula, we find f = 1/(1/v + 1/u) = 1/(1/30 - 1/10) = 5 cm.
Correct Answer: A — 5 cm
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Q. A lens forms a real image at a distance of 40 cm from the lens when the object is placed at 20 cm. What is the focal length of the lens?
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
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Solution
Using the lens formula, 1/f = 1/v - 1/u. Here, v = 40 cm, u = -20 cm. Solving gives f = 10 cm.
Correct Answer: A — 10 cm
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Q. A lens forms a real image of a height 5 cm at a distance of 40 cm from the lens. If the object is placed at 20 cm from the lens, what is the height of the object?
A.
2.5 cm
B.
5 cm
C.
10 cm
D.
20 cm
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Solution
Using the magnification formula, m = h'/h = -v/u. Here, h' = 5 cm, v = 40 cm, u = -20 cm. Thus, h = (h' * u) / v = (5 * -20) / 40 = 2.5 cm.
Correct Answer: C — 10 cm
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Q. A lens forms a real image of an object placed 60 cm away from it. If the image distance is 20 cm, what is the focal length of the lens?
A.
10 cm
B.
15 cm
C.
20 cm
D.
30 cm
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Solution
Using the lens formula 1/f = 1/v - 1/u, where u = -60 cm and v = 20 cm, we find f = 30 cm.
Correct Answer: D — 30 cm
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Q. A lens forms a real image of an object placed at a distance of 60 cm from it. If the image distance is 15 cm, what is the focal length of the lens?
A.
10 cm
B.
12 cm
C.
20 cm
D.
25 cm
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Solution
Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/15 - 1/60. Solving gives f = 10 cm.
Correct Answer: A — 10 cm
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Q. A lens forms a real image that is three times the size of the object. If the object is placed 20 cm from the lens, what is the focal length of the lens?
A.
10 cm
B.
15 cm
C.
5 cm
D.
20 cm
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Solution
Using magnification m = -v/u = 3, we find v = -60 cm and then use the lens formula to find f = 15 cm.
Correct Answer: B — 15 cm
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Q. A lens forms a real image that is twice the size of the object. If the object is placed 10 cm from the lens, what is the focal length of the lens?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Using the lens formula and magnification, we find the focal length to be 15 cm.
Correct Answer: C — 15 cm
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Q. A lens forms a virtual image at a distance of 10 cm when the object is placed at 5 cm. What type of lens is it?
A.
Convex lens
B.
Concave lens
C.
Bifocal lens
D.
Plano-convex lens
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Solution
A virtual image is formed by a concave lens when the object is placed within its focal length.
Correct Answer: B — Concave lens
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Q. A lens forms a virtual image at a distance of 12 cm when the object is placed at 8 cm. What is the focal length of the lens?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
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Solution
Using the lens formula, 1/f = 1/v - 1/u, we find f = 4 cm.
Correct Answer: A — 4 cm
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Q. A lens forms a virtual image at a distance of 20 cm from the lens when the object is placed at 10 cm. What is the focal length of the lens?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Using the lens formula 1/f = 1/v - 1/u, where v = -20 cm and u = -10 cm, we find f = 5 cm.
Correct Answer: A — 5 cm
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Q. A lens forms a virtual image at a distance of 20 cm when the object is placed at 10 cm. What is the type of lens?
A.
Convex lens
B.
Concave lens
C.
Bifocal lens
D.
Plano-convex lens
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Solution
A virtual image formed by a lens indicates that it is a concave lens.
Correct Answer: B — Concave lens
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Q. A lens has a focal length of +20 cm. What type of lens is it?
A.
Concave lens
B.
Convex lens
C.
Bifocal lens
D.
Cylindrical lens
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Solution
A positive focal length indicates that the lens is a convex lens, which converges light rays.
Correct Answer: B — Convex lens
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Q. A lens has a focal length of -10 cm. What type of lens is it?
A.
Convex lens
B.
Concave lens
C.
Biconvex lens
D.
Biconcave lens
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Solution
A negative focal length indicates that the lens is a concave lens.
Correct Answer: B — Concave lens
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Q. A lens has a focal length of 40 cm. If an object is placed 80 cm from the lens, what is the image distance?
A.
40 cm
B.
60 cm
C.
80 cm
D.
100 cm
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Solution
Using the lens formula, we find the image distance to be 40 cm.
Correct Answer: A — 40 cm
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Q. A lens has a focal length of 50 cm. If an object is placed at 100 cm, what type of image is formed?
A.
Real and inverted
B.
Virtual and erect
C.
Real and erect
D.
Virtual and inverted
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Solution
Since the object distance is greater than the focal length, a real and inverted image is formed.
Correct Answer: A — Real and inverted
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Q. A lens has a power of +2 diopters. What is its focal length?
A.
0.5 m
B.
1 m
C.
2 m
D.
3 m
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Solution
Power (P) is given by P = 1/f (in meters). Thus, f = 1/P = 1/2 = 0.5 m.
Correct Answer: B — 1 m
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Q. A lens has a power of +2.0 D. What is its focal length?
A.
50 cm
B.
25 cm
C.
20 cm
D.
10 cm
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Solution
Power (P) = 1/f (in meters), so f = 1/2.0 = 0.5 m = 50 cm.
Correct Answer: B — 25 cm
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Q. A lens has a power of +2.5 D. What is its focal length?
A.
40 cm
B.
25 cm
C.
50 cm
D.
20 cm
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Solution
Power (P) = 1/f (in meters). Therefore, f = 1/2.5 = 0.4 m = 40 cm.
Correct Answer: B — 25 cm
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Q. A lens has a power of +2.5 D. What is the focal length of the lens in meters?
A.
0.4 m
B.
0.5 m
C.
0.6 m
D.
0.7 m
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Solution
Power (P) = 1/f, so f = 1/P = 1/2.5 = 0.4 m.
Correct Answer: B — 0.5 m
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Q. A lens has a power of +5 diopters. What is its focal length?
A.
20 cm
B.
25 cm
C.
30 cm
D.
15 cm
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Solution
Power (P) = 1/f (in meters). Therefore, f = 1/P = 1/5 = 0.2 m = 20 cm.
Correct Answer: A — 20 cm
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Q. A lens has a power of -4 D. What is the type of lens?
A.
Convex
B.
Concave
C.
Bifocal
D.
Plano-convex
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Solution
A negative power indicates a concave lens.
Correct Answer: B — Concave
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Q. A lens has a power of -4 D. What type of lens is it?
A.
Convex lens
B.
Concave lens
C.
Bifocal lens
D.
Plano-convex lens
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Solution
A negative power indicates that the lens is a concave lens.
Correct Answer: B — Concave lens
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