Achromatic prism: Why subtract both angles of deflection?

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SUMMARY

The discussion centers on the calculation of the angle of deflection for an achromatic prism, specifically the formula δ = δ1 - δ2, where δ1 and δ2 represent the angles of deflection of the individual triangular prisms. This subtraction occurs because one prism bends the light beam downwards while the other bends it upwards, resulting in a net directional effect that is the angular difference between the two prisms. Additionally, this subtraction cancels chromatic variations, ensuring the prism's achromatic properties.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Familiarity with the concept of angle of deflection
  • Knowledge of triangular prism geometry
  • Basic principles of light refraction
NEXT STEPS
  • Study the derivation of Snell's Law and its applications in optics
  • Explore the properties and applications of achromatic prisms in optical devices
  • Investigate the effects of chromatic aberration in lenses and prisms
  • Learn about the design and function of optical systems using multiple prisms
USEFUL FOR

Students of optics, physicists, and optical engineers who are interested in understanding the principles of light refraction and the functionality of achromatic prisms.

HastiM
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Hello,

suppose we are given an achromatic prism consisting of two triangular prisms put together as it is shown on this webpage: http://www.schoolphysics.co.uk/age1.../text/Achromatic_prisms_and_lenses/index.html

Imagine a light beam is send through the prism. My book claims that the angle of deflection of the light beam due to the achromatic prism is given by the value δ = δ1 - δ2, where δ1, δ2 correspond to the angles of deflection of the triangular prisms. That claim is not explained at all, and I would really like to understand why the angles of deflection are just subtracted. Is it possible to deduce this formula from more elementary principles, for example from Snell's law?

I would very appreciate any help!
 
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One prism bends the ray of light down before the next prism (opposed or inverted) bends the ray of light up again.
The net directional effect is the angular difference of the two prisms.
The subtraction also cancels the chromatic variations, which makes it achromatic.
 
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