There is an equiconvex lens of focal length of 40 cm of the lens is cut into two equal parts perpel dicular to the principal axis, the focal lengths of each part will be:
There is an equiconvex lens of focal length of 40 cm of the lens is cut into two equal parts perpel dicular to the principal axis, the focal lengths of each part will be:
The correct option is A 30 cm
Let the focal length
of one separated lens be f1. This is a Plano convex lens. Now, we use lens
maker formula for f1.
1/f1=(n-1)(1/R1)……………….(1).
Here, n is refractive index of material of the
lens. R1 is radius of curvature of it’s curved surface. We have taken it
positive. It is on the object side. The second half has it’s flat surface on
object side and hence it’s curved surface has negative sign. If it’s focal
length is f2 ,then,
1/f2=(n-1)(-1/R2)……………..(2)
Adding eq.(1) and
eq.(2), we have,
1/f1+1/f2=(n-1)[(1/R1-(1/R2)]………..(3)
If f is focal length
of the original lens then right hand side of eq.(3) suggest that
1/f=1/f1
+1/f2…………………………(4)
But, original lens has
been given as equi convex. Then R1=R2 ( in value). Now, eqs.(1) and(2) suggest
f1=f2. Using this fact in eq.(4), we have, 1/f=2/f1=2/f2. Or
1/15=2/f1. Then, f1=f2=30.
Let the focal length of one separated lens be f1. This is a Plano convex lens. Now, we use lens maker formula for f1.
1/f1=(n-1)(1/R1)……………….(1).
Here, n is refractive index of material of the lens. R1 is radius of curvature of it’s curved surface. We have taken it positive. It is on the object side. The second half has it’s flat surface on object side and hence it’s curved surface has negative sign. If it’s focal length is f2 ,then,
1/f2=(n-1)(-1/R2)……………..(2)
Adding eq.(1) and eq.(2), we have,
1/f1+1/f2=(n-1)[(1/R1-(1/R2)]………..(3)
If f is focal length of the original lens then right hand side of eq.(3) suggest that
1/f=1/f1 +1/f2…………………………(4)
But, original lens has been given as equi convex. Then R1=R2 ( in value). Now, eqs.(1) and(2) suggest f1=f2. Using this fact in eq.(4), we have, 1/f=2/f1=2/f2. Or
1/15=2/f1. Then, f1=f2=30.
