Angle of minimum deviation, δm = 40° and angle of the prism, A = 60° Refractive index of water, μ = 1.33 and refractive index of the material of the prism =μ' The angle of deviation is related to refractive index (μ') as: μ' = [sin (A+δm)/2]/sin A/2 = [sin (60°+40°)/2]/sin 60°/2 = [sin (50°)]/sin 30Read more
Angle of minimum deviation, δm = 40° and angle of the prism, A = 60°
Refractive index of water, μ = 1.33 and refractive index of the material of the prism =μ’
The angle of deviation is related to refractive index (μ’) as:
μ’ = [sin (A+δm)/2]/sin A/2
= [sin (60°+40°)/2]/sin 60°/2
= [sin (50°)]/sin 30°= 1.532
Hence, the refractive index of the material of the prism is 1.532.
Since the prism is placed in water, let δ’m be the new angle of minimum deviation for the same prism. The refractive index of glass with respect to water is given by the relation:
μgw = μ’/μ = [sin (A+δ’m)/2]/sin A/2
=> [sin (A+δ’m)/2] = μ’/μ x (sin A/2)
=> [sin (A+δ’m)/2] = 1.532/1.33 x sin 60°/2= 0.5759
=> (A+δ’m)/2 = sin⁻10.5759=35.16°
60° +δ’m = 70.32°
Therefore ,
δ’m = 70.32° – 60°
= 10.32°
Hence, the new minimum angle of deviation is 10.32°.
As per the given figure, for the glass - air interface: Angle of incidence, i = 60° Angle of refraction, r = 35° The relative refractive index of glass with respect to air is given by Snell's law as: μga= sin i/sin r = sin 60°/sin 35°= 0.8660/0.5736 = 1.51 --------------Eq-1 As per the given figure,Read more
As per the given figure, for the glass – air interface:
Angle of incidence, i = 60°
Angle of refraction, r = 35°
The relative refractive index of glass with respect to air is given by Snell’s law as:
μga= sin i/sin r
= sin 60°/sin 35°= 0.8660/0.5736 = 1.51 ————–Eq-1
As per the given figure, for the air-water interface:
Angle of incidence, i = 60°
Angle of refraction r= 47°
The relative refractive index of water with respect to air is given by Snell’s law as :
μwa= sin i/sin r
= sin 60°/sin 47°= 0.8660/0.7314 = 1.184————–Eq-2
Using (1) and (2), the relative refractive index of glass with respect to water can be obtained as:
μgw = μga/μwa
=1.51/1.184= 1.275
The following figure shows the situation involving the glass – water interface.
Angle of incidence, i = 45°
Angle of refraction = r
From Snell’s law, r can be calculated as:
sin i/sin r= μgw
=>sin 45°/sin r = 1.275
sin r = (1/√2)/1.275 = 0.5546
Therefore ,r = sin⁻¹ (0.5546)
= 38.68°
Hence, the angle of refraction at the water – glass interface is 38.68°.
Actual depth of the needle in water, hi = 12.5 cm and apparent depth of the needle in water, h2 = 9.4 cm Refractive index of water = μ The value of μ can be obtained as follows: μ = h₁/h₂ = 12.5/9.4 ≈ 1.33 Hence, the refractive index of water is about 1.33. When water is replaced by a liquid of refrRead more
Actual depth of the needle in water, hi = 12.5 cm and apparent depth of the needle in water, h2 = 9.4 cm
Refractive index of water = μ
The value of μ can be obtained as follows:
μ = h₁/h₂ = 12.5/9.4 ≈ 1.33
Hence, the refractive index of water is about 1.33.
When water is replaced by a liquid of refractive index, μ’ = 1.63
The actual depth of the needle remains the same, but its apparent depth changes.
Let y be the new apparent depth of the needle. Hence, we can write the relation:
μ’= h₁/y
=> y = h₁/μ’ = 12.5/1.63 = 7.67 cm
Hence, the new apparent depth of the needle is 7.67 cm. It is less than h2. Therefore, to focus the needle again, the microscope should be moved up.
Therefore, distance by which the microscope should be moved up = 9.4 – 7.67 = 1.73 cm
Height of the needle, h1 = 4.5 cm Object distance, u = -12 cm Focal length of the convex mirror, f = 15 cm Image distance = v The value of v can be obtained using the mirror formula: 1/u + 1/v = 1/f 1/v = 1/f -1/u 1/v = 1/15 - (1/-12) = 1/15 + 1/12 = (4+5 )/60 = 9/60 Therefore , v = 60/9 = 6.7 cm HeRead more
Height of the needle, h1 = 4.5 cm
Object distance, u = -12 cm
Focal length of the convex mirror, f = 15 cm
Image distance = v
The value of v can be obtained using the mirror formula:
1/u + 1/v = 1/f
1/v = 1/f -1/u
1/v = 1/15 – (1/-12)
= 1/15 + 1/12 = (4+5 )/60 = 9/60
Therefore , v = 60/9 = 6.7 cm
Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.
The image size is given by the magnification formula:
m = h2/h1= -v/u
Therefore , h2 = -v/u x h1
=(-6.7/-12) x 4.5 = + 2.5 cm
Hence, magnification of the image, m = h2/h1 = 2.5/4.5 = 0.56
The height of the image is 2.5 cm. The positive sign indicates that the image is erect, virtual, and diminished.
If the needle is moved farther from the mirror, the image will also move away from the mirror, and the size of the image will reduce gradually.
Size of the candle, h = 2.5 cm Image size = h' Object distance, u = -27 cm Radius of curvature of the concave mirror, R = -36 cm Focal length of the concave mirror, f =R /2 = -18 cm Image distance = v The image distance can be obtained using the mirror formula: 1/f= 1/u + 1/v Read more
Size of the candle, h = 2.5 cm
Image size = h’
Object distance, u = -27 cm
Radius of curvature of the concave mirror, R = -36 cm
Focal length of the concave mirror, f =R /2 = -18 cm
Image distance = v
The image distance can be obtained using the mirror formula:
1/f= 1/u + 1/v “
=> 1/v = 1/f -1/u = 1/-18 – 1/-27= -1/54
=> v = —54 cm
Therefore, the screen should be placed 54 cm away from the mirror to obtain a sharp image.
The magnification of the image is given as:
m’ = h’/h = -v/u
Therefore , h’ = -v/u x h
= – (-54/-27) x 2.5 = -5 cm
The height of the candle’s image is 5 cm. The negative sign indicates that the image is inverted and virtual.
If the candle is moved closer to the mirror, then the screen will have to be moved away from the mirror in order to obtain the image.
A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be 40°. What is the refractive index of the material of the prism? The refracting angle of the prism is 60°. If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.
Angle of minimum deviation, δm = 40° and angle of the prism, A = 60° Refractive index of water, μ = 1.33 and refractive index of the material of the prism =μ' The angle of deviation is related to refractive index (μ') as: μ' = [sin (A+δm)/2]/sin A/2 = [sin (60°+40°)/2]/sin 60°/2 = [sin (50°)]/sin 30Read more
Angle of minimum deviation, δm = 40° and angle of the prism, A = 60°
Refractive index of water, μ = 1.33 and refractive index of the material of the prism =μ’
The angle of deviation is related to refractive index (μ’) as:
μ’ = [sin (A+δm)/2]/sin A/2
= [sin (60°+40°)/2]/sin 60°/2
= [sin (50°)]/sin 30°= 1.532
Hence, the refractive index of the material of the prism is 1.532.
Since the prism is placed in water, let δ’m be the new angle of minimum deviation for the same prism. The refractive index of glass with respect to water is given by the relation:
μgw = μ’/μ = [sin (A+δ’m)/2]/sin A/2
=> [sin (A+δ’m)/2] = μ’/μ x (sin A/2)
=> [sin (A+δ’m)/2] = 1.532/1.33 x sin 60°/2= 0.5759
=> (A+δ’m)/2 = sin⁻10.5759=35.16°
60° +δ’m = 70.32°
Therefore ,
δ’m = 70.32° – 60°
= 10.32°
Hence, the new minimum angle of deviation is 10.32°.
See lessFigures 9.34(a) and (b) show refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in glass when the angle of incidence in water is 45s with the normal to a water- glass interface [Fig. 9.34(c)].
As per the given figure, for the glass - air interface: Angle of incidence, i = 60° Angle of refraction, r = 35° The relative refractive index of glass with respect to air is given by Snell's law as: μga= sin i/sin r = sin 60°/sin 35°= 0.8660/0.5736 = 1.51 --------------Eq-1 As per the given figure,Read more
As per the given figure, for the glass – air interface:
Angle of incidence, i = 60°
Angle of refraction, r = 35°
The relative refractive index of glass with respect to air is given by Snell’s law as:
μga= sin i/sin r
= sin 60°/sin 35°= 0.8660/0.5736 = 1.51 ————–Eq-1
As per the given figure, for the air-water interface:
Angle of incidence, i = 60°
Angle of refraction r= 47°
The relative refractive index of water with respect to air is given by Snell’s law as :
μwa= sin i/sin r
= sin 60°/sin 47°= 0.8660/0.7314 = 1.184————–Eq-2
Using (1) and (2), the relative refractive index of glass with respect to water can be obtained as:
μgw = μga/μwa
=1.51/1.184= 1.275
The following figure shows the situation involving the glass – water interface.
Angle of incidence, i = 45°
Angle of refraction = r
From Snell’s law, r can be calculated as:
sin i/sin r= μgw
=>sin 45°/sin r = 1.275
sin r = (1/√2)/1.275 = 0.5546
Therefore ,r = sin⁻¹ (0.5546)
= 38.68°
Hence, the angle of refraction at the water – glass interface is 38.68°.
See lessA tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?
Actual depth of the needle in water, hi = 12.5 cm and apparent depth of the needle in water, h2 = 9.4 cm Refractive index of water = μ The value of μ can be obtained as follows: μ = h₁/h₂ = 12.5/9.4 ≈ 1.33 Hence, the refractive index of water is about 1.33. When water is replaced by a liquid of refrRead more
Actual depth of the needle in water, hi = 12.5 cm and apparent depth of the needle in water, h2 = 9.4 cm
Refractive index of water = μ
The value of μ can be obtained as follows:
μ = h₁/h₂ = 12.5/9.4 ≈ 1.33
Hence, the refractive index of water is about 1.33.
When water is replaced by a liquid of refractive index, μ’ = 1.63
The actual depth of the needle remains the same, but its apparent depth changes.
Let y be the new apparent depth of the needle. Hence, we can write the relation:
μ’= h₁/y
=> y = h₁/μ’ = 12.5/1.63 = 7.67 cm
Hence, the new apparent depth of the needle is 7.67 cm. It is less than h2. Therefore, to focus the needle again, the microscope should be moved up.
Therefore, distance by which the microscope should be moved up = 9.4 – 7.67 = 1.73 cm
See lessA 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
Height of the needle, h1 = 4.5 cm Object distance, u = -12 cm Focal length of the convex mirror, f = 15 cm Image distance = v The value of v can be obtained using the mirror formula: 1/u + 1/v = 1/f 1/v = 1/f -1/u 1/v = 1/15 - (1/-12) = 1/15 + 1/12 = (4+5 )/60 = 9/60 Therefore , v = 60/9 = 6.7 cm HeRead more
Height of the needle, h1 = 4.5 cm
Object distance, u = -12 cm
Focal length of the convex mirror, f = 15 cm
Image distance = v
The value of v can be obtained using the mirror formula:
1/u + 1/v = 1/f
1/v = 1/f -1/u
1/v = 1/15 – (1/-12)
= 1/15 + 1/12 = (4+5 )/60 = 9/60
Therefore , v = 60/9 = 6.7 cm
Hence, the image of the needle is 6.7 cm away from the mirror. Also, it is on the other side of the mirror.
The image size is given by the magnification formula:
m = h2/h1= -v/u
Therefore , h2 = -v/u x h1
=(-6.7/-12) x 4.5 = + 2.5 cm
Hence, magnification of the image, m = h2/h1 = 2.5/4.5 = 0.56
The height of the image is 2.5 cm. The positive sign indicates that the image is erect, virtual, and diminished.
If the needle is moved farther from the mirror, the image will also move away from the mirror, and the size of the image will reduce gradually.
See lessA small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
Size of the candle, h = 2.5 cm Image size = h' Object distance, u = -27 cm Radius of curvature of the concave mirror, R = -36 cm Focal length of the concave mirror, f =R /2 = -18 cm Image distance = v The image distance can be obtained using the mirror formula: 1/f= 1/u + 1/v Read more
Size of the candle, h = 2.5 cm
Image size = h’
Object distance, u = -27 cm
Radius of curvature of the concave mirror, R = -36 cm
Focal length of the concave mirror, f =R /2 = -18 cm
Image distance = v
The image distance can be obtained using the mirror formula:
1/f= 1/u + 1/v “
=> 1/v = 1/f -1/u = 1/-18 – 1/-27= -1/54
=> v = —54 cm
Therefore, the screen should be placed 54 cm away from the mirror to obtain a sharp image.
The magnification of the image is given as:
m’ = h’/h = -v/u
Therefore , h’ = -v/u x h
= – (-54/-27) x 2.5 = -5 cm
The height of the candle’s image is 5 cm. The negative sign indicates that the image is inverted and virtual.
If the candle is moved closer to the mirror, then the screen will have to be moved away from the mirror in order to obtain the image.
See less