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Given
Virtual image area = 6.25 mm2
Actual ara = 1 mm2
We can calculate linear magnification as
we also know
Now, according to the lens formula
and
Since the image is forming at a distance which is less than 25 cm, it can not be seen by eye distinctively.

a)
maximum magnifying is possible when our image distance will be equal to minimum vision point that is,
(Given)
Now according to the lens formula
Hence required object distance for viewing squares distinctly is 7.14 cm away from the lens.
b)
Magnification of the lens:
c)
Magnifying power
Since the image is forming at near point ( d = 25 cm ), both magnifying power and...

Given
The focal length of the convex lens
here liquid is acting like the mirror so,
the focal length of the liquid
the focal length of the system(convex + liquid)
Equivalent focal length when two optical systems are in contact
Now, let us assume refractive index of the lens be
The radius of curvature are and .
As we know,
Now, let refractive index of liquid be
The radius of...

Given
Angle of deflection
The distance of the screen from the mirror
The reflected rays will bet deflected by twice angle of deviation that is
Now from the figure, it can be seen that
Hence displacement of the reflected spot of the light is .

Given,
Distance between the objective mirror and secondary mirror
The radius of curvature of the Objective Mirror
So the focal length of the objective mirror
The radius of curvature of the secondary mirror
so, the focal length of the secondary mirror
The image of an object which is placed at infinity, in the objective mirror, will behave like a virtual object for the secondary...

Given, image is formed at a distance = 25cm
As we know, magnification of eyepiece lens is given by :
Now,
Height of the final image is given by :
Therefore, the height of the final image will be 28.2 cm

Given,
focal length of the objectove lens = = 140cm
focal length of the eyepiece lens = = 5 cm
Height of tower = 100m
Distance of object which is acting like a object = 3km = 3000m.
The angle subtended by the tower at the telescope
Now, let the height of the image of the tower by the objective lens is .
angle made by the image by the objective lens :
Since both, the angles are the same...

a) Given,
focal length of the objective lens = = 140cm
focal length of the eyepiece lens = = 5 cm
The separation between the objective lens and eyepiece lens is given by:
Hence, under normal adjustment separation between two lenses of the telescope is 145 cm.

Given,
the focal length of the objective lens
the focal length of the eyepiece lens
normally, least distance of vision = 25cm
Now,
as we know magnifying power when the image is at d = 25 cm is
Hence magnification, in this case, is 33.6.

Given,
the focal length of the objective lens
the focal length of the eyepiece lens
normally, least distance of vision = 25cm
Now,
As we know magnifying power:
Hence magnifying power is 28.

Given,
magnifying power = 30
objective lens focal length
= 1.25cm
eyepiece lens focal length
= 5 cm
Normally, image is formed at distance d = 25cm
Now, by the formula;
Angular magnification by eyepiece:
From here, magnification by the objective lens :
since ( )
According to the lens formula:
from here,
hence object must be 1.5 cm away from the objective lens.
Now for the...

When we view through a compound microscope, our eyes should be positioned a short distance away from the eyepiece lens for seeing a clearer image. The image of the objective lens in the eyepiece lens is the position for best viewing. It is also called "eye-ring" and all reflected rays from lens pass through it which makes it the ideal position for the eye for the best view.
When we put our eyes...

We need more magnifying power and angular magnifying power in a microscope in order to use it effectively. Keeping both objective focal length and eyepiece focal length small makes the magnifying power greater and more effective.

Firstly, grinding a lens with very small focal length is not easy and secondly and more importantly, when we reduce the focal length of a lens, spherical and chronic aberration becomes more noticeable. they both are defects of the image, resulting from the ways of rays of light.

Yes, angular magnification will change if we move our eye away from the lens. this is because then angle subtended by lens would be different than the angle subtended by eye. When we move our eye form lens, angular magnification decreases. Also, one more important point here is that object distance does not have any effect on angular magnification.

Angular magnification is the ratio of tangents of the angle formed by object and image from the centre point of the lens. In this question angle formed by the object and a virtual image is same but it provides magnification in a way that, whenever we have object place before 25cm, the lens magnifies it and make it in the vision range. By using magnification we can put the object closer to the...

Given,
Object distance u = -9cm
Focal length of convex lens = 10cm
According to the lens formula
a) Magnification
The area of each square in the virtual image
b) Magnifying power
c) No,
.
Both the quantities will be equal only when image is located at the near point |v| = 25 cm

Given
Object height = 1.5 cm
Object distance from convex lens = -40cm
According to lens formula
Magnificatio due to convex lens:
The image of convex lens will act as an object for concave lens,
so,
Magnification due to concave lens :
The combined magnification:
Hence height of the image =
= 0.652 * 1.5 = 0.98cm
Hence height of image is 0.98cm.

Let prism be ABC ,
as emergent angle ,
(approx)
Now as we know in the prism
Hence,
Now applying snells law at surface AB
Hence the angle of incident is 29.75 degree.

Here there are two cases, first one is the one when we see it from convex side i.e. Light are coming form infinite and going into convex lens first and then goes to concave lens afterwords. The second case is a just reverse of the first case i.e. light rays are going in concave first.
1)When light is incident on convex lens first
Now this will act as an object for the concave...

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