List the sign conventions that are followed in case of refraction of light through spherical lenses. Draw a diagram and apply these conventions in determining the nature and focal length of a spherical lens which forms three times magnified real image of an object placed 16 cm from the lens.

Sign convention for the refraction of light is as follows.

1. All the distances are measured from the optical centre of the lens.


2. All the distances which are measured in the same direction of the incident light ray (left hand side of lens) will be taken as positive.


3. All the distances which are measured against the direction of incident light (right hand side) are taken as negative.


4. The perpendicular distances to principal axis in upward direction will be positive and those in downward direction will be taken as negative.


Figure below illustrates the conventions more clearly.


According to the question.


Magnification (m) = -3 (real image is always inverted).


Object distance (u) = -16cm.


By Magnification Formula;


Magnification,


Where,


v is the image distance,


u is the object distance



v= -16 × -3


v= 48cm.


Image distance (v) = 48cm.


By lens formula;







Therefore the focal length is 12 cm. Since the focal length is positive, therefore the lens is convex lens.


Figure below shows the ray diagram for the same.



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