Here in this post, we shall calculate the formation of mirror.This a very mile topic Brainimatic Series will throw for physics students and anybody that offer science. This post will you some formula to calculate an illuminated object.
Experimental (focal length of curve mirror)
We all know that a screen in the form of a sheet of paper is move in front of the mirror until the sharpest image of a window forms on the object. The distance in between the screen and the mirror is measured and this gives an approximate value of the focal length of the mirror.
To experiments more, as the window is far from the mirror, the rays from it may be considered as parallel rays especially when they strike the mirror. They will therefore come to a focus after reflection at the principal focus
Focal length from measurement of the radius of curvature
By the Use of Search pin and the method of no - parallax
An object pin is stick into a cork and attached to a stand. The concave mirror and the optical pin are arranged well. The pin is move up and down until it coincides with it's image p when viewed from above. At this position there is no parallax between the pin and its inverted image as seen in the mirror.
The distance between the pin and the mirror gives the value of r. The focal length f is obtained from the relation
r
f ------------
2
By the Use of the mirror equation
1 1 1
---------- + --------- = ----------
u v f
The equation can be used to obtain the focal length of a concave mirror. An approximate focal length value is first obtained as already discussed. An illuminated object ( the Cross wire of a ray box) is placed at a distance of about
3
------------ in front of the mirror.
2
The exact distance is measured and recorded as u. The screen position is adjusted until a sharp image is obtained . The distance from the mirror to that of screen is measured and recorded as v . The experiment is repeated for various object distances, u, and the corresponding values of v are obtained. The value of f can be obtained by substituting the values of u and v to the mirror formula and finding the average value of f or by plotting the value of
1 1
---------- against -------------
u v
The intercept on either axis is equal to
1
--------------- the reciprocal of this intercept
f
gives the value of the focal length of the mirror.
Sign convention
when the mirror formula is used in solving practical problem, it is necessary to add a positive numbers (+) or a negative (-) sign to each of the distance according to a sign rule or convention.
Two commonly used sign convention are below:
(1)Real is positive
(2) New Cartesian
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Real is positive
---------------------------
(a) Real object and real images are considered to be at a positive distance from the mirror
-------------------------------------
New Cartesian
--------------------------------------
(a) Distances measured to the right the mirror are positive
--------------------------------------
Real is positive
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(b) Virtuous images are at negative distance from the mirror
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(b) Distance measured to the left of the mirror are negative
Now, let look at the formula of linear magnification (M) produced by a mirror
v height of image
M = ---------- = ----------------------------------
u height of object
The above formula is linear magnification of the mirror.Let look at some examples
Example
An object is placed 10 in front of a concave mirror whose radius of curvature is 12cm. Calculate the position, nature and the magnification of the image produced
Solution
Real - is - positive
r. 12
f =+ ---------------- = + ----------------
2. 2
u = +6 cm, u = + 10 cm
Using the formula below
1. 1 1
-------------- + -------------- = --------------
v. u. f
1 1 1
= ------------- - ------------ = --------------
6 10 15
v = + 15 cm
since v is + be, image is real
v 15
m = ------------- = ---------------
u 10
= 1 . 5
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