Concept explainers
The difference in angular dispersion.
Answer to Problem 24P
The difference in angular dispersion is
Explanation of Solution
Write the expression for Snell’s law of refraction at the air-silica flint glass interface.
Here,
Rearrange the above equation to find
Given that the refractive index of the air is
The above equation is written as
For the incoming violet ray the above equation is written as
Here,
For the incoming red ray the equation (III) is written as
Here,
Write the expression for Snell’s law of refraction at the silica flint glass-air interface.
Here,
Rearrange the above equation to find
For the outgoing violet ray the above equation is written as
Here,
For the incoming red ray the equation (III) is written as
Here,
Write the expression for sum of all the angles in the Triangle for the outgoing rays in Figure P25.23.
Here,
Rearrange the above equation to find
Use equation (X) in (VIII).
Use equation (IV) in (XI).
Use equation (VIII) in (IX).
Use equation (V) in (XIII).
Write the expression for difference in angular dispersion.
Use equation (XII) and (XIV) in equation (XV).
Conclusion:
Therefore, the difference in angular dispersion is
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Chapter 25 Solutions
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