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Q.

In an experiment with a rectangular glass slab, for an angle of incidence of{"mathml":"<math class="image_resized" style="width:24px;height:11px"><span style="font-family:in air, angle of refraction is measured to be {"mathml":"<math class="image_resized" style="width:14px;height:12px"><span style="font-family: . When the glass slab is replaced by a hollow slab filled with water, angle of refraction is measured to be {"mathml":"<math class="image_resized" style="width:14px;height:12px"><span style="font-family:. Then:


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a

{"mathml":"<math class="image_resized" style="width:39px;height:12px"><span style="font-family: 

b

{"mathml":"<math class="image_resized" style="width:43px;height:15px"><span style="font-family: 

c

{"mathml":"<math class="image_resized" style="width:51px;height:15px"><span style="font-family: 

d

None of the above 

answer is B.

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Detailed Solution

Concept: Snell's law may be used to determine the relationship between the angle of refraction and the refractive index of the medium. We may compare the refractive indices of glass and water after establishing a relationship between them, and then utilize our relationship to examine the angle of refraction in other media.
Question ImageIn the given problem, the first medium is air (refractive index =1) andQuestion Image. For the first case, the second medium is glass slab. So, we can write
Question Imagewhere Question Image is the refractive index of glass and Question Image is angle of refraction.
Question ImageFor the second case, the second medium is water. So, we can write
Question Imagewhere Question Image is the refractive index of glass and Question Image is the angle of refraction.
Question ImageDividing equation 1 and 2
Question ImageWe know that refractive index of water (1.33) is less than refractive index of glass (1.5) Therefore mathematically we can write,Question ImageSo,
Question ImagePutting value of Question Image from equation 3 , we get
Question ImageQuestion ImageSince, sine is an increasing function, if sine of some value is greater than sine of other value then the value (with greater sine) will be greater than the value (with smaller sine). So, we can say
Question ImageHence, the correct option is 2.
 
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