A shaft of light pass through the prism

In summary, when a shaft of light passes through a prism with refracting angle \theta and refractive index n, and the light passes through the prism symmetrically, the deviation angle \alpha is the least. This is demonstrated by assuming an apex angle for the prism and using the fact that interior angles in a triangle sum to 180 to relate the refracting angles on each face of the prism. By setting the derivative of the deflection angle as a function of the refracting angle equal to 0, it can be shown that \alpha is the least when the light passes through the prism symmetrically.
  • #1
thee
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0
A shaft of light passes through a prism with refracting angle [tex] \theta [/tex] and refractive index [tex] n [/tex]. Let [tex] \alpha [/tex] be the deviation angle of the shaft. Demonstrate that if the shaft of light passes through the prism symetrically the angle [tex] \alpha [/tex] is the least?
 
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  • #2
thee said:
A shaft of light passes through a prism with refracting angle [tex] \theta [/tex] and refractive index [tex] n [/tex]. Let [tex] \alpha [/tex] be the deviation angle of the shaft. Demonstrate that if the shaft of light passes through the prism symetrically the angle [tex] \alpha [/tex] is the least?

The least in regards to what?

-Dan
 
  • #3
picture

I suppose that [tex] \beta [/tex] is the refracting angle

I think that it try to proove that [tex]\beta[/tex] is equal to [tex] \theta [/tex] angle [tex] \alpha [/tex] will become the least.
 

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  • #4
"passes through symmetrically" means that the path inside the prism
is parallel to the face of the prism that isn't used as a window ...
that is, theta_glass on face 2 = - theta_glass on face 1.

You'll probably want to assume an "apex" angle for the prism
and recall that the interior angles in a triangle sum to 180,
to relate the theta_glass on face 2 to the theta_glass on face 1.

With the deflection angle as a function of theta_glass, set the derivitive =0.
 

Related to A shaft of light pass through the prism

What is a prism?

A prism is a transparent, solid object with two ends that are parallel and congruent polygons, and the remaining sides are parallelograms. It is commonly made of glass or plastic and is used to refract or split white light into its component colors.

How does a prism work?

A prism works by refracting, or bending, light as it passes through the different densities of materials. When white light enters the prism, it is split into its component colors (red, orange, yellow, green, blue, indigo, and violet) due to their different wavelengths.

Why is a shaft of light passed through a prism?

A shaft of light is passed through a prism to demonstrate the process of refraction and to show how white light can be split into its component colors. This is also commonly used in experiments and demonstrations to study the properties of light.

What happens to a shaft of light when it passes through a prism?

When a shaft of light passes through a prism, it is refracted or bent at different angles depending on the wavelength of each color. This results in the separation of the white light into its component colors, creating a rainbow-like effect.

How is a prism used in everyday life?

Prisms have many practical applications in everyday life. They are commonly used in optical devices such as cameras, binoculars, and telescopes to help focus and magnify images. They are also used in spectacles and sunglasses to correct vision and reduce glare. In addition, prisms are used in scientific experiments and in the production of rainbows in nature and in art.

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