Ray Optics And Optical Instruments

According to mirror formula

Here and


As the object moves at a constant speed of after the new position of image is



The shift in the position of image in is

Average speed of image

Focal length of converging lens

From lens formula

or

or
Magnification,
Apparent area of card through lens

According to lens makers formula

Here, (For plane surface)

;
or

Magnification
Focal length of co-axial combination



Hence, lens is convex lens.

In the figure


using

Suppose initial height of the water level was . Initial position of the observer was and final position is

Now for the image to be formed at the same place.
From adjacent figure

(Object distance should be same)





Water level increased by .

A convex mirror is used for this purpose
According to mirror formula
Differentiate w.r.t. time



Also to find

For first lens

To find
Using lens formula



For second lens


Again using lens formula




Final image will be formed at to the right of second lens

Let be the centre and and the poles of the sphere.
ray parallel to a diameter is first refracted into the glass along .
For refraction at from air to glass, we have

Here
and

Concave mirror with radius
Convex mirror with radius
Focus,
Focus,

From mirror formula,

From concave minor, the image formed by minor will be








The image will be out of reflecting surface of mirror . So, this will be the final image and it will form on the left of .