The object 5cm high is placed in front of a lens of power +2D. Two times real and magnified image of the object is attained by the lens.

Find 1)Object distance

2)Image distance

3)height of the image

Asked by katariayash1212 | 17th Jun, 2020, 01:06: PM

Expert Answer:

ho = 5 cm 
P = + 2D 
f = 1/2 = 0.5 m = 50 cm 
 
Magnification, 
m = - 2 ...(as real and magnified image is formed) 
 
i) Object distance
m space equals space fraction numerator i m a g e space d i s tan c e thin space left parenthesis v right parenthesis over denominator o b j e c t space d i s tan c e space left parenthesis u right parenthesis space end fraction
minus 2 space space equals space space v over u
v space equals negative 2 u space... space left parenthesis 1 right parenthesis

B y space l e n s space f o r m u l a comma space
1 over v space minus 1 over u space equals space 1 over f
1 over 50 equals space fraction numerator 1 over denominator negative 2 u end fraction minus 1 over u
1 over 50 space equals space fraction numerator u plus 2 u over denominator negative 2 u squared end fraction space equals space fraction numerator 3 over denominator negative 2 u end fraction
u space equals space fraction numerator 3 over denominator negative 2 end fraction cross times 50 space equals space minus 75 space c m space
T h u s comma space o b j e c t space d i s tan c e space i s space minus space 75 space c m space

i i right parenthesis space I m a g e space d i s tan c e
f r o m space e q space left parenthesis 1 right parenthesis comma space
v space equals negative 2 u space
v space equals space minus 2 open parentheses negative 75 close parentheses space equals 150 space c m space space
T h u s comma space i m a g e space d i s tan c e comma space v space equals 150 space c m space


i i i right parenthesis space H e i g h t space o f space i m a g e space left parenthesis h subscript i right parenthesis space
m space equals space h subscript i over h subscript o
minus 2 space equals space h subscript i over 5 space
rightwards double arrow h subscript i space space equals space minus 10 space c m
N e g a t i v e space s i g n space i n d i c a t e s space t h a t space t h e space i n v e r t e d space i m a g e space i f space f o r m e d. space space
 
 

Answered by Shiwani Sawant | 17th Jun, 2020, 10:50: PM