Question
i.) Derive the lens formula, 1/ f = 1/v – 1/u for a concave lens, using the necessary ray diagram.
ii.) How does the angle of minimum deviation of a glass prism of refractive index 1.15 change, if it is immersed in a liquid of refractive index 1.3?
Solution
i.) Derivation of len's formula :
Len's formula gives us the relation between focal length of a lens and distances of object and image from the optical centre of the lens.
Let's consider a convex lens and O be the optical centre ; F the principal focus with focal length f.
Len's formula gives us the relation between focal length of a lens and distances of object and image from the optical centre of the lens.
Let's consider a convex lens and O be the optical centre ; F the principal focus with focal length f.
Let, AB be the object held perpendicular to the principal axis at a distance beyond the focal length of the lens. And, as seen from the fig. above a real, inverted and magnified image A'B' is formed.
We can see that, .
and also,
But, OC = AB
From the above equations, we get
Using the sign convention,
OB= -u , OB' = +v, OF = +f
Dividing both sides by uvf, we have
i.e.,
which is the required lens formula.
ii.) Given, a glass prism of refractive index = 1.5
When, this prism is immersed in a liquid of refractive index 1.3 then, angle of minimum deviation of the prism reduces.
We can see that, .
and also,
But, OC = AB
From the above equations, we get
Using the sign convention,
OB= -u , OB' = +v, OF = +f
Dividing both sides by uvf, we have
i.e.,
which is the required lens formula.
ii.) Given, a glass prism of refractive index = 1.5
When, this prism is immersed in a liquid of refractive index 1.3 then, angle of minimum deviation of the prism reduces.
