5. An illuminated object lies at a distance 1.0 m from a screen. A convex lens is used to form an image of the object on a screen placed at a distance of 75 cm from the lens. Find : (i) the focal length of the lens, and (ii) the magnfication. Ans. (i) 18.75 cm (i) – 3 -
Answers
Answer:
As we know, the lens formula is —
\dfrac{1}{v} – \dfrac{1}{u} = \dfrac{1}{f} \\[0.5em]
v
1
–
u
1
=
f
1
Given,
Object lies at a distance 1.0 m from a screen.
v = 75 cm
So, u = - 25 cm
Substituting the values in the formula, we get,
\dfrac{1}{75} – \dfrac{1}{-25} = \dfrac{1}{f} \\[0.5em] \dfrac{1}{75} + \dfrac{1}{25} = \dfrac{1}{f} \\[0.5em] \dfrac{1+3}{75} = \dfrac{1}{f} \\[0.5em] \dfrac{4}{75} = \dfrac{1}{f}\\[0.5em] \Rightarrow f = \dfrac{75}{4} \\[0.5em] \Rightarrow f = \text{18.75 cm} \\[0.5em]
75
1
–
−25
1
=
f
1
75
1
+
25
1
=
f
1
75
1+3
=
f
1
75
4
=
f
1
⇒f=
4
75
⇒f=18.75 cm
Therefore, focal length of the lens is 18.75cm.
ii) As we know,
the formula for magnification of a lens is —
m = \dfrac{v}{u} \\[0.5em]m=
u
v
Given,
v = 75 cm
u = - 25 cm
Substituting the values in the formula, we get,
m = \dfrac{75}{-25} \\[0.5em] m = -3 \\[0.5em]m=
−25
75
m=−3
Therefore, the magnification is -3.
Step-by-step explanation: