Reflection and Refraction

Reflection and refraction

When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray.

Reflection

The law of reflection says that the reflected ray lies in the plane of incidence, and the angle of reflection equals the angle of incidence.

Refraction

Refraction is the bending of light rays when passing through a surface between one transparent material and another.

It is described by Snell’s Law:

n1 sinθ1 = n2 sinθ2

where

θ1 is the angle between the ray and the surface normal in the first medium (the angle of refraction)

θ2 is the angle between the ray and the surface normal in the second medium (the angle of incidence)

n1 and n2 are the indices of refraction, n = 1 in a vacuum and n > 1 in a transparent substance.

This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:

v1 sinθ2 = v2 sinθ1

where v1 and v2 are the wave velocities through the respective media.

Lens : A device which produces converging or diverging light rays due to refraction is known as a lens.

The equation that determines the location of the images given a particular focal length (f) and object distance (S1):

1/S1 + 1/S2 = 1/f

where S2 is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side of the lens.

The focal length f is considered negative for concave lenses.

The magnification of a lens is given by

M = – S2 / S1 = f / (f-S1)

lenses are placed in contact: if the lenses of focal lengths f1 and f2 are “thin”, the combined focal length f of the lenses is given by

1/f = 1/f1 +1/f2

If two thin lenses are separated in air by some distance d, the focal length for the combined system is given by

1/f = 1/f1 +1/f2 – d / f1f2

Index of Refraction:

Materials of greater density have a higher index of refraction.

n = c / v

where

n = index of refraction

c = speed of light in a vacuum

v = speed of light in the material

n=λ0 / λm

where

λ0 = wavelength of the light in a vacuum

λn = its wavelength in the material

Critical Angle:

The maximum angle of incidence for which light can move from n1 to n2

sinθc = n2 / n1 for n1 > n2

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