Math, asked by pradeepsethshg2, 21 hours ago

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

Answered by vvsns0266
0

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:

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