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As we know that the relation between focal length , the distance between screen and distance between two locations of the object is :
Given: = 90 cm., = 20 cm ,
so
Hence the focal length of the convex lens is 21.39 cm.

As we know for real image, the maximum focal length is given by
where d is the distance between the object and the lens.
So putting values we get,
Hence maximum focal length required is 0.75.

We use diamond as a cutter because it is very hard and sharp. The refractive index is high in diamond ensures that light goes through multiple total internal reflections so that light goes in all direction. This is the reason behind the shining of the diamond. Light entering is totally reflected from faces before it getting out, hence producing a sparkling effect

Yes, appearing depth of water will decrease when we view obliquely, this happens because of the fact that light bends from its direction whenever it goes from one medium to another medium.

The diver is in denser medium (water) and fisherman is in lighter medium (air). As the diver is looking at the fisherman, rays of light will go from fisherman to divers eye, that is, from lighter medium to denser medium. Since rays deflect toward normal when it goes form lighter to a denser medium, the fisherman will look taller than actual to the diver.

No, there is no contradiction. A virtual image is formed whenever the light rays are diverging. We have a convex lens in our eye. This convex lens converges the diverging rays into our retina and forms a real image. In other words, the virtual image acts as an object to the convex lens of our eye to form a real image, which we see on the screen called retina.

If our object is virtual then Plane and convex mirrors can produce a real image. That is, when the light coming from infinity goes into the convex mirror, it creates a virtual object behind the convex mirror. the reflection of this virtual object in the convex mirror can be taken out on screen and hence convex mirror can make a real image.

In the case when there is no outer layer,
Snell's law at glass-air interface(when the ray is emerging out from the pipe)
36.5
refractive angle corresponding to this = 90 - 36.5 = 53.5.
the angle r is greater than the critical angle
So for all of the incident angles, the rays will get total internally reflected.in other words, rays won't bend in air-glass interference, it would rather hit...

We are given,
Refractive index of glass() and outer covering() is 1.68 and 1.44 respectively.
Now applying snell's law on upper glass - outer layer,
the angle from where total Internal reflection starts
At this angle, in the air-glass interface
Refraction angle = 90 - 59 = 31 degree
let Incident Angle be .
Applying Snell's law
(approx)
Hence total range of incident angle for which...

As we know,
Refractive index =
Here actual depth = 15cm
let apparent depth be d'
And refractive index of the glass = 1.5
now putting these values, we get,
the change in the apparent depth = 15 - 10 = 5 cm.
as long as we are not taking slab away from the line of sight of the pin, the apparent depth does not depend on the location of the slab.

The focal length of concave mirror is always negative.
Also conventionally object distance is always negative.
So we have mirror equation:
Now in this equation whenever , will always be positive which means is always positive which means it lies on the right side of the mirror which means image is always virtual.
Now,
since the denominator is always less than the numerator, so the...

In a convex mirror focal length is positive conventionally.
so we have mirror equation
here since is positive and is negative (conventionally) so we have,
that is '
which means the image will always lie between pole and focus.
Now,
here since is always negative conventionally, it can be seen that magnification of the image will be always less than 1 and hence we conclude that image...

In a convex mirror focal length is positive conventionally.
so we have mirror equation
Here, since object distance is always negative whenever we put our object in the left side of the convex mirror(which we always do, generally). So is always the sum of two positive quantity(negative sign in the equation and negative sign of the will always make positive) and hence we conclude...

The equation we have for a mirror is:
Given condition and
and
Here has to be negative in order to satisfy the equation and hence we conclude that our mirror is a concave Mirror. It also satisfies that (image lies beyond 2f)

Given,
The radius of the lunar orbit,r = .
The diameter of the moon,d =
focal length
let be the diameter of the image of the moon which is formed by the objective lens.
Now,
the angle subtended by diameter of the moon will be equal to the angle subtended by the image,
Hence the required diameter is 13.74cm.

Angular magnification in the telescope is given by :
angular magnification =
Here given,
focal length of objective length = 15m = 1500cm
the focal length of the eyepiece = 1 cm
so, angular magnification,

The magnifying power of the telescope is given by
Here, given,
focal length of objective lens = 144 cm
focal length of eyepiece lens = 6 cm
Hence magnifying power of the telescope is 24.
in the telescope distance between the objective and eyepiece, the lens is given by
Therefore, the distance between the two lenses is 250 cm.

Inside a microscope,
For the eyepiece lens,
we are given
we can also find this value by finding image distance in the objective lens.
So, in objective lens
we are given
Distance between object lens and eyepiece = = 2.27 + 7.2 = 9.47 cm.
Now,
Magnifying power :
Hence magnifying power for this case will be 88.

In a compound microscope, first, the image of an object is made by the objective lens and then this image acts as an object for eyepiece lens.
Given
the focal length of objective lens = = 2 cm
focal length of eyepiece lense = = 6.25cm
Distance between the objective lens and eyepiece lens = 15 cm
a)
Now in Eyepiece lense
Image distance = = -25 cm (least distance of vision with sign...

When two lenses are in contact the equivalent is given by
where and are the focal length of two individual lenses.
SO,Given,
30 cm and (as focal length of the convex lens is positive and of the concave lens is negative by convention)
putting these values we get,
Hence equivalent focal length will be -60 cm and since it is negative,equivalent is behaving as a concave lens which is...

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