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After tracing the path of rays of light through a glass slab for three different angles of incidence, a student measured the corresponding values of angle of refraction \[r\] and the angle of emergence \[e\] and recorded them in the table given below:
S. No. \[\angle i\,\angle r\,\angle e\]
I. \[30^\circ \,20^\circ \,31^\circ \]
II. \[40^\circ \,25^\circ \,40^\circ \]
III. \[50^\circ \,31^\circ \,49^\circ \]
The correct observations are:
A. I and II
B. II and III
C. I and III
D. I, II and III

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Last updated date: 17th Jun 2024
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Answer
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Hint:First of all, we will need the conditions which gives the approximation between the values of the angle of incidence and the angle of refraction. We will also use the concept in which angle of refraction is directly proportional to the angle of incidence.

Complete answer:
To begin with, we will individually check for the conditions which are true according to the physics behind it. First of all, we will list down the conditions which will be necessary to check the observations: If the light rays pass through a glass slab, the following hold true for the observations.The angle of incidence should be approximately equal to the angle of emergence. We can write as \[\angle i \approx \angle e\] and the refracted angle is less than the angle of incidence i.e. \[\angle r < \angle i\].

The angle of refraction also increases when the angle of incidence. We can say that the angle of refraction is directly proportional to the angle of incidence.
For the observation, \[30^\circ \,20^\circ \,31^\circ \] :
\[30^\circ \approx 31^\circ \]
The angle of incidence is approximately equal to the angle of emergence.

For the observation, \[40^\circ \,25^\circ \,40^\circ \] :
\[40^\circ = 40^\circ \]
The angle of incidence is equal to the angle of emergence.

For the observation, \[50^\circ \,31^\circ \,49^\circ \] :
\[50^\circ \approx 49^\circ \]
The angle of incidence is approximately equal to the angle of emergence.

Hence, we can say that the conditions are satisfied for all the three observations. The correct option is D.

Additional information:
Refraction is the bending of a wave when it passes from one medium to another. The bending is caused due to the differences in density between the two substances.Hence, we can define;refraction is the change in the direction of a wave passing from one medium to another.Laws of refraction state that:
-The incident ray refracted ray, and the normal to the interface of two media at the point of incidence all lie on the same plane.
-The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. This is also known as Snell’s law of refraction.

Note: While answering this question, most of the students seem to have a confusion regarding the angle of incidence and the angle of emergence. The incident angle is the angle at which the light ray falls on the glass slab. The emergent angle is the angle at which the light rays exits the glass slab after going through refraction of light inside the glass slab.