A a concave lens has focal length of 15cm at what distance should be the object placed from the lens so that it is formed and image at 10 cm from the lens? What will be the nature and  magnification of the image

Asked by malkabaswarai | 27th Mar, 2020, 12:07: PM

Expert Answer:

If a concave  lens has  focal length of 15 cm then the  distance of that object from the lens such that it forms an image  at 10 cm from the  lens is calculated as follows: 

begin mathsize 12px style straight u space colon negative space the space object space distance
straight v space colon negative space the space image space distance
straight f space colon negative the space focal space length space of space straight a space lens
B y space l e n s space f o r m u l a comma space
1 over straight v minus 1 over straight u equals 1 over straight f
As space the space lens space is space concave comma space the space image space so space formed space is space always space vir t ual comma space therefore space apostrophe straight v apostrophe space is space negative.
Also comma space the space focal space length space of space straight a space concave space lens space is space negative.
minus 1 over 10 minus 1 over straight u equals negative 1 over 15
minus 1 over straight u equals negative 1 over 15 plus 1 over 10
1 over straight u equals fraction numerator negative 10 plus 15 over denominator 150 end fraction equals 5 over 150 equals 1 over 30
straight u equals negative 30 space cm


end style
The magnification of lens is
begin mathsize 12px style Magnification space left parenthesis straight M right parenthesis equals negative straight v over straight u equals negative fraction numerator 10 over denominator negative 30 end fraction equals 1 third end style 
As, magnification is less than 1 the size of image is less than object size.
The image formed by concave lens is at same side as that of object. 
Thus, nature of image is virtual, erect and diminished. 

Answered by Shiwani Sawant | 27th Mar, 2020, 01:08: PM