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Mirror formula is considered one of the most asked concept.
24 Questions around this concept.
In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is :
A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen :
You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :
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A concave mirror of focal length 'f1' is placed at a distance of 'd' from a convex lens of focal length 'f2'. A beam of light coming from infinity and falling on this convex lens - concave mirror combination returns to infinity. The distance 'd' must equal:
Match the corresponding entries of column 1 with column 2 [where m is the magnification produced by the mirror]
Column 1 |
Column 2 |
(A) m = -2 |
(a) Convex mirror |
(B) |
(b) Concave mirror |
(C) m = +2 |
(c) Real image |
(D) |
(d) Virtual image |
A thin rod of length is placed along the optical axis of a concave mirror of focal length such that its image which is real and elongated just touches the rod. Calculate the magnification.
Mirror formula
Similarly, In and
From (i) &(ii)
Now, ;
Put these value in above relation:
Proved.
Magnification in Spherical mirrors:
lateral magnification:
The lateral magnification is defined as the ratio:
To compute the vertical magnification, consider the extended object OA shown in Figure. The base of the object, O will map
on to a point I on the principal axis which can be determined from the equation .
The image of the top of the object A, will map on to a point A' that will lie on the perpendicular through I. The exact location can be determined by drawing a ray from A passing through the pole and intercepting the line through I at A'.
Consider the triangles APO and A'PI in the figure. As the two
triangles are similar, we get,
Applying the sign convention, we get, u=-PO
Therefore,
magnification formula can be modified as:
Longitudinal magnification: When object lies along the principal axis then its axial magnification 'm' is given by
If the object is small,
Relation between velocity of object and mirror in Spherical mirror
Case I: when the object moves along principal axis
When we differentiate equation with respect to time.
= velocity of image w.r.t. miror
= velocity of object w.r.t. mirror
Therefore, when mirror is at rest along the principal axis.
Case II: when the object moves perpendicular to principal axis
When an Object is moving perpendicular to the principal axis. This time (image distance) and (object distance) are constant.
Therefore we have the following relation :
Also, x-coordinates of both image and object remain constant. On differentiating the above relation w.r.t time we get,
Here, denotes velocity of object perpendicular to the principal axis and denotes velocity of the image perpendicular to the principal axis.
Hence we can conclude that,
Newton's Formula:
As we know that the mirror formula is given as
Let's assume, x = distance of the object from focus
y = distance of the image from focus
Newton's formula is useful for calculating the image position for a curved mirror.
The diagram shows the position of an object and its image formed by a concave mirror.
Let the distances of the object and image from the principal focus of the mirror be x and y respectively.
Then: Object distance (u) = f+x and Image distance (v) = f+y
Using the mirror formula we have:
and simplifying this we get:
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