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Geometrical Optics (Reflection)

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Q.

Two objects A and B, when placed in turn in front of a concave mirror of focal length 7.5 cm give images of equal size. If A is two times the size ofB and is placed at a distance of 15cm from the mirror, find the distance ofB from the mirror

Q.

A 4.5 cm long needle is placed 12 cm from a convex mirror of focal length 15 cm. find the location and the length of the image of the needle. What happens when the needle is moved farther from the mirror 

Q.

A square wire of side 3.0 cm is placed 25 cm away from a concave mirror of focal length 10 cm. What is the area enclosed by the image of the wire? The centre of the wire is on the axis of the mirror, with its two sides normal to the axis.  

Q.

In the figure shown, the focal length of the two thin convex lenses is the samef. They are separated by a horizontal distance 3f and their optical axis are displaced by a vertical separation ‘d’ (d << f), as shown. Taking the origin of coordinates O at the centre of the first lens, the x and y coordinates of the point where a parallel beam of rays coming from the left finally get focused, are given by :

                                                                

Q. In the following question: A bullet of mass m2 is fired from a gun of mass m1 with horizontal velocity v. A plane mirror us fixed at gun facing towards bullet. The velocity of image of bullet formed by the plane mirror with respect to bullet is I am unable to understand how v(i) is different from v(ib) that is w.r .t bullet. ?

if the velocity of bullet is v in + direction i.e = +v
then velocity of image will be = -v
thus velocity of image wrt original bullet will be = -v - (+v)
= -2v
i.e twice will be the velocity

Q. The wavelength of light diminishes μ times in the medium. A diver from inside water (μ = 1.33) looks at an object whose natural colour is green. He sees the object as?

We know that on entering water, the wavelength decreases. Hence, the green colour appears blue.

Q. On changing the meduim why the wavelength decrease??

The energy of the light is related to the frequency; when the light enters the medium there are interference patterns that cause the apperent speed of light to change; if the frequency changed, the energy would not be conserved. The wavelength changes to balance the change in speed.

Mathematically,The velocity of light in a given medium is obtained by the equation v equals nu lambda where 'nu' is the frequency of light and 'lambda' is its wavelength in that medium. Velocity of light is directly proportional to the wavelength.

Q. A terrestrial telescope is made by introducing an erecting lens of focal length f between the objective and eye-piece lenses of an astronomical telescope. This causes the length of the telescope tube to increase by an amount equal to?

The minimum distance between the real object and real images is 4f.

The minimum distance between the real object and real images is 4f.

If in the astronomical telescope ,a lens of short focal length f is placed at 2f from intermediate image,it will erect intermediate image at a distance 2f on the other side of it and this image will act as an object for eye lens. This causes the length of the telescope tube to increase by an amount equal to 4f.

Q. A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angle to the plane of the mirror through 20o, the angle between the incident ray and new reflected ray is 45o. The angle between the incident ray and original reflected ray is?

When mirror rotated through an angle θ about an axis in the plane of mirror then reflection ray rotated through an angle 2θ perpendicular to the plane of mirror the angle of incidence and angle of reflection does not change.

Q. A CONVERGING MIRRROR M1, A POINT SOURCE S AND A DIVERGING MIRROR M2 ARE ARRANGED . THE SOURCE IS PLACED AT A DISTANCE OF 30 cm FROM M1. THE FOCAL LENGTH OF EACH OF THE MIRRORS IS 20 cm . CONSIDER ONLY THE IMAGES FORMED BY A MAXIMUM OF TWO REFLECTIONS.
IT IS FOUND THAT ONE IMAGE IS FORMED ON THE SOURCE ITSELF.
A) FIND THE DISTANCE BETWEEN THE TWO MIRRORS.
B) FIND THE LOCATION OF THE IMAGE FORMED BY THE SINGLE REFLECTION FROM M2.?

One image is formed on the object so distance between object and mirror M2 is 20 cm Hence distance between M1 and M2 is 50 cm.
again for mirror M2
u=-20 cm
f=20 cm
from mirror
1/u +1/v =1/f
v=10 cm
so image is formed 10 cm behind the mirror M2