Question

In an experiment to measure the focal length (f) of a concave mirror, the object distance (x) and image distance (y) measured as (24.0 ± 0.1) cm and (12.0 ± 0.1) cm respectively, then

Answer 1

ANSWER :

1.75

• See image attached

MORE:

• The focal length of a lens is determined when the lens is focused at infinity. Lens focal length tells us the angle of view—how much of the scene will be captured—and the magnification—how large individual elements will be. The longer the focal length, the narrower the angle of view and the higher the magnification.

• The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light.

Answer 2

GIVEN,

Object distance x= (24.0±0.1)

image distance y= (12.0±0.1)

TO FIND,

the focal length (f)

SOLUTION,

we are given x and y, we shall use the mirror formula,

$\frac{1}{v} +\frac{1}{u} =\frac{1}{f}$---------------------1

substituting values,

$\frac{1}{24} +\frac{1}{12} =\frac{1}{f}\\\\\frac{1+3}{24} =\frac{1}{f}\\\\\frac{4}{24}=\frac{1}{f}$

∴f= 6cm

after differentiating eq 1 we have,

$\frac{-df}{f^{2} }= \frac{-du}{u^{2} }- \frac{dv}{v^{2} }$

this can also be written as,

|Δf|max= $| \frac{|u|}{u^{2} } +\frac{ |v|}{v^{2} } | f^{2}$

substituting the values we get,

|Δf| max = $| \frac{0.1}{24^{2} } +\frac{0.1}{12^{2} }| (6)^{2}$

|F|= 0.0008680*36

|F|= 0.03125.

now F= 6+ 0.03125= 6.03125cm

HENCE THE FOCAL LENGTH IS 6.03125CM.