The magnifying power of a simple microscope is given b y1+D/f,where D is the least distance for clear vision. For farsighted persons, D is greater than the usual. Does it mean that the magnifying power of a simple microscope is greater for a farsighted person as compared to a normal person? Does it mean that a farsighted person can see an insect more clearly under a microscope than a normal person?
Answers
The magnifying power of a simple microscope is given by 1+D/f,
But magnifying power depends on ratio D/f
where D is the D for a farsighted person is greater than that for a normal person, but the value of f remains the same.
Hence magnifying power of a simple microscope is greater for a farsighted person compared to that for a person with normal vision.
yes , the farsighted person can see an insect more clearly under a microscope than a normal person
Answer:
(a) Ray diagram : - (Ref. image).
(b) Expression for magnifying power: The ratio of the visual angle of image to the visual angle of object, placed at the least distance of distinct vision, is called magnifying power.
m=
Visual angle of object placed at the least distance of distinct vision
Visual angle of image
or m=
α
β
As the angles α and β are small.
Therefore, m=
tanα
tanβ
......(i)
In ΔAOB, tanβ=
OB
AB
and in ΔA
′′
OB
′
,
tanα=
B
′
O
A
′′
B
′
∴ m=
A
′′
B
′
/B
′
O
AB/OB
or m=
OB
AB
×
AB
D
(∵A
′′
B
′
=AB and BO=D=Least distance of distinct vision)
Or m=
OB
D
By sign convention, D will be negative and OB=−u.
∴ m=
−u
−D
Or m=
u
D
.....(i)
Where, u is the distance of object from the lens.
(i) when the image is formed distinct vision at the least distance of:
from lens formula,
f
1
=
v
1
−
u
1
f
1
=
−v
1
−
−u
1
(from sign convention)
Or
f
1
=
v
−1
+
u
1
But v=D= Least distance of distinct vision
∴
f
1
=
D
−1
+
u
1
Or
f
D
=−1+
u
D
Or 1+
f
D
=
u
D
Putting the value in equation (ii)
m=1+
f
D
(ii) When the image is formed at infinity:
u=f
From equation (i) m=
f
D
For greater magnification, focal length should be small.