UG Astronomy - Unit III Refraction

1. Astronomy
PREPARED BY
MS. R. UMADEVI
ASSISTANT PROFESSOR
DEPARTMENT OF MATHEMATICS
BON SECOURS COLLEGE FOR WOMEN
THANJAVUR

3.  Refraction is the change in the direction of a wave passing from
one medium to another.
 If a ray of light passes from one medium to another its course is
deviated either towards or away from the normal at the point of
incidence. This deviation is called refraction of light.
 When a ray of light passes from a rarer medium to a denser one
the refraction is towards the common normal and the refraction is
away from the common normal if the ray of light passes from a
denser to a rarer medium
Refraction

4. Laws of refraction
(i)The incident ray, the refracted ray and the
normal at the point of incidence are all in the
same plane.
(ii)The sine of the angle of incidence is in a constant
ratio to the sine of the angle of refraction for a
particular pair of media. This constant is called
“ refractive index” and it is denoted by μ.
μ =
sin θ2
sin θ1

5. Astronomical Refraction
 The earth is surrounded by a number of layers of atmosphere
extending to a height of about one hundred and fifty kilometers.
 A ray of light starting from a celestial body after travelling through
vacuum is incident at the outermost layer of the atmosphere.
 It gets refracted in the successive layers and reaches the observer in a
direction other than the direction in which it started.
 This deviation of light is called Astronomical refraction or
Atmospheric refraction.

6. Example :
When a celestial body (the sun, stars, moon, or
planets), appears to an observer on earth to be
in a slightly different position than its actual
geometric position. The actual position of the
sun when this picture was taken was below the
horizon, or nearly so. When a celestial body is
low on the horizon, the light from it has to
travel through the Earth’s atmosphere, which
causes it to be refracted or bent. Because of the
low position in the sky, the light must pass
through much more of the Earth’s atmosphere
than when the object is higher in the sky.
Location, Ocean Shores, WA. Lower lobe
touched the horizon at 7:11:11 PM PDT,
September 22, 2018. Refracted cloud
silhouettes starting to appear across the
face of the sun.

7. Tangent Formula for Refraction
Let us assume that the earth is flat and that it
is surrounded by a number of heterogeneous
layers of atmosphere.
Let a ray of light starting from a star X after
travelling in vacuum be incident on the outer
most layer of the atmosphere. Let i be the
angle of incidence. The ray is refracted in the
successive layers so that it reaches the
observer at earth’s surface. Let r1, r2,….. be
the angles of refraction in the successive
layers.

8. At the layer immediately above the surface of the earth the angle of
refraction is the same as the apparent zenith distance z of the star.
Let μ1, μ2, μ3…….. be the refractive indices of the successive layers and
μ that of the surface of earth with respect to vaccum so that
sin i = μ1 sin r1 = μ2 sin r2 = ………… = μ sin z
⸫ sin i = μ sin z …………. (1)
Let r be the amount of refraction
i = z + r
(1) becomes sin ( z + r ) = μ sin z
sin z cos r + cos z sin r = μ sin z
r is very small ⸫ sin r = r , cos r = 1

9. ⸫ sin z + r cos z = μ sin z
r cos z = μ sin z – sin z
r cos z = ( μ – 1 ) sin z
r = ( μ – 1 )
sin 𝑧
cos 𝑧
r = ( μ – 1 ) tanz
Put ( μ – 1 ) = k
r = k tan z
This is known as the tangent formula for refraction. k is called the
coefficient of refraction.

10. General Effects of Refraction
 Due to refraction the position of a celestial body is apparently
shifted towards the zenith along the vertical through the body through
a distance equal to the amount of refraction.
 The altitude is increased.
 Zenith distance decreased.
 Bodies nearer the horizon are more affected than those nearer the
zenith.
 Azimuth of a body is unaffected.
 Time of transit are unaffected by refraction.

11. Horizontal Refraction
 Due to refraction the apparent position of a body is elevated towards
the zenith.
 Therefore in order to get the true position of the body its apparent
position must be depressed through a distance k tanz or A tanz +
Btan3z.
 If a body is very near horizon its zenith distance is about 900
 Therefore both tanz or A tanz + Btan3z are infinitely large.
 This is absurd.

12.  Therefore both tangent formula and cassini’s formula cannot be
applied to objects near horizon.
Both formulae can be applied to zenith distances only upto about 750
The refraction for objects very near horizon has been calculated by
some other methods.
This refraction is called the horizontal refraction.
Its value is about 34’.