Ray Optics and Optical Instruments
- If fV and fR are the focal lengths of a convex lens for violet and red light respectively and FV and FR are the focal lengths of concave lens for violet and red light respectively, then we have
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1 = (μ - 1) 
1 - 1 
f R1 R2
According to Cauchy relationμ = A + B + C .... Hence f ∝ λ λ2 λ4
Hence, red light having maximum wavelength has maximum focal length.
∴ fv < fr and also Fv > Fr as focal length is negative for a concave lens.Correct Option: A
1 = (μ - 1) 1 - 1 f R1 R2
According to Cauchy relationμ = A + B + C .... Hence f ∝ λ λ2 λ4
Hence, red light having maximum wavelength has maximum focal length.
∴ fv < fr and also Fv > Fr as focal length is negative for a concave lens.
- A convex lens of focal length 80 cm and a concave lens of focal length 50 cm are combined together. What will be their resulting power?
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We know that
1 = 1 + 1 ; f1 = 80 cm, f2 = –50 cm f f1 f2 1 = 1 - 1 f 80 50 100 100 ⇒ P = 1 = 1.25 - 2 = -0.75 D f Correct Option: D
We know that
1 = 1 + 1 ; f1 = 80 cm, f2 = –50 cm f f1 f2 1 = 1 - 1 f 80 50 100 100 ⇒ P = 1 = 1.25 - 2 = -0.75 D f
- A ray of light is incident at an angle of incidence, i, on one face of prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is µ, the angle of incidence i, is nearly equal to :
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For normally emerge e = 0
Therefore r2 = 0 and r1 = A
Snell’s Law for Incident ray’s
1sin i = µ sin r1 = µsin A
For small angle i = µACorrect Option: A
For normally emerge e = 0
Therefore r2 = 0 and r1 = A
Snell’s Law for Incident ray’s
1sin i = µ sin r1 = µsin A
For small angle i = µA
- A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it?
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For the lens,1 - 1 = 1 ; 1 - 1 = 1 ⇒ v = 60 cm v u f v -30 20
Coincidence is possible when the image is formed at the centre of curvature of the mirror. Only then the rays refracting through the lens will fall normally on the convex mirror and retrace their path to form the image at O. So, the distance between lens and mirror = 60 – 10 = 50 cm.Correct Option: C
For the lens,1 - 1 = 1 ; 1 - 1 = 1 ⇒ v = 60 cm v u f v -30 20
Coincidence is possible when the image is formed at the centre of curvature of the mirror. Only then the rays refracting through the lens will fall normally on the convex mirror and retrace their path to form the image at O. So, the distance between lens and mirror = 60 – 10 = 50 cm.
- A plano-convex lens is made of material of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is
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R1 = 60 cm, R2 = , µ = 1.6
1 = (μ - 1) 1 - 1 f R1 R2 1 = (1.6 - 1) 1 ⇒ f = 100 cm f 60
Correct Option: B
R1 = 60 cm, R2 = , µ = 1.6
1 = (μ - 1) 1 - 1 f R1 R2 1 = (1.6 - 1) 1 ⇒ f = 100 cm f 60
R1 = 60 cm, R2 = , µ = 1.61 = (μ - 1) 1 - 1 f R1 R2 1 = (1.6 - 1) 1 ⇒ f = 100 cm f 60
