Define magnifying power of a telescope. Write its expression.
A small telescope has an objective lens of focal length 150 cm and an eye piece of focal length 5 cm. If this telescope is used to view a 100 m high tower 3 km away, find the height of the final image when it is formed 25 cm away from the eye piece.
a) Magnifying power of telescope is the ratio of the angle subtended at the eye by the image to the angle subtended at the unaided eye by the object.
Mathematically, we can write
where, fo is the focal length of the objective, fe is the focal length of the eye-piece and D is the least distance of distinct vision.
b) Using, the lens equation for objective lens,
Hence, magnification due to the objective lens is given by,
Now, using lens formula for eye-piece, we get
Therefore, magnification due to eyepiece me = 
Hence, total magnification, 
So, size of final image = 
(a) Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism.
Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation.
(b) Explain briefly how the phenomenon of total internal reflection is used in fiber optics.
a) The phenomenon of refraction for a ray of monochromatic light passing through a glass prism is shown as below: 
Let, PQR be the principal section of the prism.
The refracting angle of prism is A. Monochromatic light EF is incident on face PQ at angle of incidence i1. This ray enters from a rarer to denser medium and hence is refracted towards the normal FN. Refracted ray is FG. Angle of refraction for this face is r1. Refracted ray FG becomes incident on face PR and is refracted away from the normal GN2 and emerges in the direction GH. The angle of incidence on this face is r2 (into prism) and angle of refraction (into air) is i2. At point O, incident and the emergent ray meet. The angle between these two rays is called the angle of deviation ‘
’. 
.
... (1)
The normal FN1 and GN2 on faces PQ and PR respectively, when produced meet at N.
Let, 
... (2) 
We can see that, for one angle of deviation we have two angles of incidence. But, angle of deviation is minimum for only one particular angle if incidence. Angle of minimum deviation is denoted by 
.
So let, i1 = i2 = i
And r1 = r2 = r
Therefore, we have (4) and (6), we have
b) An optical fiber is a device based on total internal reflection by which a light signal may be transmitted from one place to another with a negligible loss of energy. When a light ray is incident on one end at a small angle of incidence, it suffers refraction from air to quartz and strikes the quartz-coating interface at an angle more than the critical angle. Hence, total internal reflection happens and the ray of light strikes the opposite face again at an angle greater than critical angle. The phenomenon of total internal reflection takes place. Thus the ray within the fiber suffers multiple total internal reflections and finally strikes the other end at an angle less than critical angle for quartz-air interface and emerges in air.
An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears:
10 times taller.
10 times nearer.
20 times taller.
20 times taller.
C.
20 times taller.
The height of image depends upon magnifying rows to see 20 times taller object, angular magnification should be 20 and we observe angular magnification option (c) would not be very correct as the telescope can be adjusted to form the image anywhere between infinity and least distance for distinct vision.Suppose that the image is formed at infinity. Then. the observer will have to focus the eyes at infinity to observe the image. Hence, it is incorrect to say that the image will appear nearer to the observer.
In an experiment for determination of refractive index of glass of a prism by i− δ, plot, it was found that a ray incident at angle 35o, suffers a deviation of 408 and that it emerges at angle 79o ⋅ Ιn that case which of the following is closest to the maximum possible value of the refractive index?
1.5
1.6
1.7
1.7
A.
1.5
C.
1.7
If μ is the refractive index of the material of prism, the from shell's law
This angle is greater than the 40o and deviation angle already given. For greaterμ deviation will be even higher. Hence μ of the given prism should be lesser than 1.5. Hence, the closest option will be 1.5
A pipe open at both ends has a fundamental frequency f in the air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:
f/2
3f/4
2f
2f
D.
2f
For open ends, fundamental frequency f in air
we have
When a pipe is dipped vertically in the water, so that half of it is in water, we have
Thus, the fundamental frequency of the air column is now,
f=f'
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