Question

Derive the mathematical equation of magnification of a simple Microscope

Answer 1

M =

b/a

---------(1)

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since

a

and

b

are small angles, therefore we can take:

a

= tan

a

.

and

.

b

= tan

b

$M=\frac{tan\beta }{tan\alpha }$

-------------------(2)

Consider an object OP placed at a distance "p" within the focal length of a magnifying glass such that an erect ,virtual and magnified image IQ is produced at 25 cm from the eye.

In right angled triangle

D

ABE:

tan

a

= AB/EB

-----

OR

tan

a

= AB/d---------(a)

In right angled triangle

D

OPE:

tan

b

= OP/PE

-----

tan

b

= OP/p-------(b)

-----

Since OP = AB = height of object

tan

b

= AB/p-------(c)

-----

Putting the values of tan

a

and tan

b

in equation (2)

M = (AB/p)/(AB/d)

M = d/p -----------------(d)

Using thin lens formula

$\frac{1}{f}= \frac{1}{p} +\frac{1}{q}$

Here P = + p, q = - d and f = + f

1/f = 1/-d + 1/p

1/f = -1/d + 1/p

Multiplying both sides by "d"

d/f = -d/d + d/p

d/f = -1 + d/p

1 + d/f = d/p

or

d/p

=

1 +

d/

f

-----(e)

Comparing equation (e) and (d)

$M=1+\frac{d}{f}$

This expression indicates that for high magnification, focal length of magnifying glass

Answer 2

heya...

Magnifying power of magnifying glass

By definition magnifying power or angular magnification of magnifying glass is the ratio of visual angle subtended by the image seen through a magnifying glass to visual angle subtended by the object when placed at the least distance of distinct vision ,when see through the naked eye.

M =

b/a

---------(1)

For latest information , free computer courses and high impact

since

a

and

b

are small angles, therefore we can take:

a

= tan

a

.

and

.

b

= tan

b

-------------------(2)

Consider an object OP placed at a distance "p" within the focal length of a magnifying glass such that an erect ,virtual and magnified image IQ is produced at 25 cm from the eye.

In right angled triangle

D

ABE:

tan

a

= AB/EB

-----

OR

tan

a

= AB/d---------(a)

In right angled triangle

D

OPE:

tan

b

= OP/PE

-----

tan

b

= OP/p-------(b)

-----

Since OP = AB = height of object

tan

b

= AB/p-------(c)

-----

Putting the values of tan

a

and tan

b

in equation (2)

M = (AB/p)/(AB/d)

M = d/p -----------------(d)

Using thin lens formula

Here P = + p, q = - d and f = + f

1/f = 1/-d + 1/p

1/f = -1/d + 1/p

Multiplying both sides by "d"

d/f = -d/d + d/p

d/f = -1 + d/p

1 + d/f = d/p

or

d/p

=

1 +

d/

f

-----(e)

Comparing equation (e) and (d)

M=1+d/f

This expression indicates that for high magnification, focal length of magnifying glass