A spherical mirror produces an image of magnification -1.0 on a screen placed at a distance of 30 cm from the pole of the mirror. a) Write the type of mirror used. b) What is the focal length of this mirror? c) Calculate the object distance. d) What is the nature of the image formed? e) Draw the ray diagram to show the image formation.

 

 

Asked by harishsrinivasan0769 | 22nd Jul, 2020, 02:40: PM

Expert Answer:

m =-1 
 
v = - 30 cm 
a) As the magnification produced due to spherical mirror is -1 it shows that the image is formed at the same side of object and of same size of object. Also it shows that the image is real and inverted. Thus, the nature of mirror is concave mirror. 
 
b)focal length of concave mirror : - 
I n space c a s e space o f space c o n c a v e space m i r r o r comma space w h e n space t h e space m a g n i f i c a t i o n space i s space minus 1 comma space i t space s h o w s space t h a t space i m a g e space d i s tan c e space a n d space o b j e c t space d i s tan c e space a s space e q u a l. space
H e r e space 30 space c m. space
I n space c a s e space o f space c o n c a v e space m i r r o r space i t space i s space p o s s i b l e space o n l y space w h e n space o b j e c t space i s
space p l a c e d space a t space t h e space c e n t r e space o f space c u r v a t u r e space left parenthesis d i s tan c e space equals space r a d i u s space o f space c u r v a t u r e right parenthesis
F o r space c o n c a v e space m i r r o r comma space
W h e n space m space equals negative 1 comma space
space i m a g e space d i s tan c e space left parenthesis v right parenthesis space equals space o b j e c t space d i s tan c e space left parenthesis u right parenthesis space equals space R a d i u s space o f space c u r v a t u r e space left parenthesis R right parenthesis space.... left parenthesis 1 right parenthesis
T h u s comma space R space equals space minus 30 space c m space
W e space k n o w comma space
R space equals space 2 f space
T h u s comma space
f space space equals space fraction numerator negative 30 over denominator 2 end fraction space equals space minus 15 space c m space... left parenthesis f o c a l space l e n g t h space o f space c o n c a v e space m i r r o r right parenthesis
c right parenthesis space O b j e c t space d i s tan c e
F r o m space left parenthesis 1 right parenthesis space i t space i s space c l e a r space t h a t space o b j e c t space d i s tan c e space left parenthesis u right parenthesis space equals space minus 30 space c m space
A n o t h e r space w a y space t o space f i n d space t h e space o b j e c t space d i s tan c e space i s space b y space u sin g space f o r m u l a space o f space l i n e a r space m a g n i f i c a t i o n space a s space f o l l o w s comma space
m space equals space minus space v over u
minus 1 space equals space minus open parentheses fraction numerator negative 30 over denominator u end fraction close parentheses
T h u s comma space u space equals space minus 30 space c m space
T h i s space m e a n s space t h e space o b j e c t space d i s tan c e space i s space 30 space c m space a n d space p l a c e d space t o space l e f t space s i d e space o f space c o n c a v e space m i r r o r. space
 
d) Image formation ray diagram: - 

Answered by Shiwani Sawant | 22nd Jul, 2020, 08:28: PM