Figure shows a ray of light meeting the glass of the
window of a car at an angle of incidence of 30o
.
(i) Assuming that the refractive index of glass is 1.5,
find the angle of refraction for this ray in the
glass. (Given : sin (19.5o
) = 1/3)
(ii) Complete the diagram by sketching the path of
the ray through the glass and out on the other
side.
(iii) Use the diagram to explain the effect of the glass
on what is seen by the driver
Answers
i. Angle of refraction = 19.5°
ii. The diagram shows refraction from the incident ray
iii. Objects are slightly displaced from their original position.
Given:
Angle of incidence = 30°
Refractive index = 1.5
To find:
i. Angle of refraction.
ii. Diagram of the ray's path through the glass and out on the other side.
iii. Effect of glass on what is seen by the driver.
Solution:
Through Snell's law, we know that light travels in the spot where it can reach faster. Reflection is where the light travels and returns. Refraction is where the light passes and bends.
Using Snell's law we know that the refractive index is equal to the ratio of the sine of the angle of incidence and the sine of the angle of refraction.
n = Sin i / Sin r
Here i = angle of incidence = 30 °
n = refractive index = 1.5
1.5 = Sin 30° / Sin r
Sin r = Sin 30° / 1.5
Sin 30° = 1/2
Sin r = 1/2 / 1.5
Sin r = 1/3
r = angle of refraction = 19.5°
ii. Diagram is attached as an image.
iii. Since the ray of light meeting in the window's glass is refracted, the object seen in the window is slightly displaced from its original position.
Therefore,
i. Angle of refraction = 19.5°
ii. The diagram shows refraction from the incident ray
iii. Objects are slightly displaced from their original position.
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Answer:
i. the angle of refraction for this ray in the glass is 19.5°.
iii. Using Snell's law, we can find the angle of refraction for the given ray of light in the glass. Snell's law states that the ratio of the sines of the angle of incidence and angle of refraction is equal to the ratio of the refractive indices of the two media.
Explanation:
(i) Using Snell's law, we can find the angle of refraction for the given ray of light in the glass. Snell's law states that the ratio of the sines of the angle of incidence and angle of refraction is equal to the ratio of the refractive indices of the two media. Mathematically, this can be written as sin i / sin r = n2 / n1, where i is the angle of incidence, r is the angle of refraction, n1 is the refractive index of the first medium (air in this case), and n2 is the refractive index of the second medium (glass in this case).
Substituting the given values, we get sin 30 / sin r = 1.5 / 1
sin r = sin 30 / 1.5
sin r = 1/3
r = sin^-1 (1/3)
r = 19.5°
Therefore, the angle of refraction for this ray in the glass is 19.5°.
(ii) To complete the diagram, we can draw a line from the point of incidence in the glass at an angle of 19.5° with the normal to the surface of the glass. This line will refract again when it emerges from the glass and enters the air at an angle equal to the angle of incidence in the glass. This line can be drawn using the same angle of incidence and the normal to the surface of the glass.
(iii) The glass of the car window bends the path of light, causing the image of an object outside the car to be displaced. The angle at which light enters the glass is different from the angle at which it exits, causing the image to appear to be in a different position than it actually is. This effect is known as refraction. In this case, the glass causes the image to appear higher than it actually is, as the angle of refraction is less than the angle of incidence. This can be observed by the driver of the car, who will see an object in a slightly different position than it actually is due to the refraction caused by the car window.
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