A ray of light is incident onto the interface between material 1 and material 2.
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Question “A ray of light is incident onto the interface between material 1 and material 2.”
A ray of light is incident onto the interface between material 1 and material 2.
Given the indices of refraction n_1 and n_2 of material 1 and material 2, respectively, rank these scenarios on the basis of the phase shift in the refracted ray.
1) Rank from largest to smallest. To rank items as equivalent, overlap them.
a) n1,water=1.33
n2,air=1.00
b) n1,water=1.33
n2,quartz=1.46
c) n1,water=1.33
n2,diamond=2.42
d) n1,air=1.00
n2,quartz=1.46
e) n1,benzene=1.50
n2,water=1.33
f) n1,air=1.00
n2,water=1.33
2) Rank these scenarios on the basis of the phase shift in the reflected ray.
a) n1,benzene=1.50
n2,water=1.33
b) n1,air=1.00
n2,quartz=1.46
c) n1,water=1.33
n2,quartz=1.46
d) n1,water=1.33
n2,air=1.00
e) n1,water=1.33
n2,diamond=2.42
f) n1,air=1.00
n2,water=1.33
Answer
To solve the problem, two concepts are used: total internal reflection and critical angles.
First, calculate the expression for the critical angle using Snell’s law. Next, calculate the critical angles for each case using the previously calculated expression of Snell’s law. Finally, arrange the results in decreasing order.
The critical angle: When the incident light ray travels through a dense medium and reaches the interface with the less dense medium, it is refracted at an angle with the normal at that interface. The critical angle of incidence is defined as an incidence angle that is 90 degrees.
Total Internal Reflection: When the angle is greater than the critical angle, the incident rays of light get completely internal reflected. This phenomenon is called total internal reflection.
Snell’s law expresses itself as follows:
Here, thi is the incidence angle, while thr the refraction angle. n2 is the refractive indices of the refraction media and n1 the refractive indices of the incident medium.
(B)
Consider th c as the critical angle of incidence
Snell’s law:
Here, n 2 is a refractive indicator of the rarer medium and n 1 the refractive Index of the denser media.
Substitute the c to replace the i and 90deg to replace the r.
Thus,
A light ray’s total internal reflection is only possible if the refractive index in the medium where it travels initially is higher than that of the interface. This means that the light travels from a dense medium to a rarer one.
Snell’law is a formula that solves for the critical angle for incidence, defined as the angle at which the refraction angle equals 90deg.
It is wrong to consider the refraction angle greater than 90deg to be the critical angle for incidence. Refer to the critical angle for an incidence angle where the refraction angle equals 90deg.
Take the expression of critical angles from step 1 to calculate the critical angle in each case. Then arrange the results in decreasing order.
Calculate the critical angle.
Case 1
Critical angle can be described as:
Substitute 1.00 to n 2 or 2.42 to n 1.
Case 2
Critical angle can be described as:
Substitute 1.33 to n 2 or 2.42 to n 1.
Case 3
Critical angle can be described as:
Substitute 1.33 to get n 2 or 1.50 to get n 1.
Case 4 :
Critical angle can be described as:
Substitute 1.33 to n 1 or 1.00 to n 2.
Part B
The critical angles in the following scenarios are listed in decreasing order
.
Take the expression of the critical incidence, obtained in step 1, and calculate the critical angle under the four conditions. Then arrange the critical angles in decreasing order.
for the expression of critical angle, as the correct expression is
.
Conclusion
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