What is the value of the focal length fn2
of a convergent lens with index of refraction ( n2 =1.5) if it was
fn1 =5cm for an index of refraction n1 = 1.4 .
To find the value of the focal length fn2 of a convergent lens with an index of refraction n2 = 1.5, given the focal length fn1 = 5cm for an index of refraction n1 = 1.4, we can use the lensmaker's formula.
The lensmaker's formula relates the focal length of a lens to the radii of curvature of its surfaces and the refractive indices of the lens material and the surrounding medium. It can be expressed as:
1/f = (n2 - n1) * (1/R1 - 1/R2)
Where:
- f is the focal length of the lens
- n1 is the refractive index of the medium on one side of the lens
- n2 is the refractive index of the lens material
- R1 and R2 are the radii of curvature of the lens surfaces
We are given that fn1 = 5cm and n1 = 1.4. We need to find fn2 when n2 = 1.5.
Substituting the given values into the lensmaker's formula:
1/fn1 = (n2 - n1) * (1/R1 - 1/R2)
Since the lens is convergent, the radius of curvature R2 will be positive. However, the radius of curvature R1 will be negative for the convex side of the lens. Therefore, we can assume R1 = -R.
1/5 = (1.5 - 1.4) * (1/R - 1/R2)
Simplifying the equation:
1/5 = 0.1/R - 0.1/R2
To find fn2, we need to find R2. Rearranging the equation:
0.1/R2 = 1/5 - 0.1/R
0.1/R2 = (1 - 0.1R)/(5R)
Cross-multiplying:
0.1 * 5R = (1 - 0.1R) * R2
0.5R = R2 - 0.1R2
0.5R = 0.9R2
Dividing both sides by 0.9R2:
0.5R / (0.9R2) = 1
0.5 / 0.9R = 1 / R2
R2 = 0.9R / 0.5
R2 = 1.8R
Therefore, the value of R2 is 1.8 times the value of R.
Since we do not have specific information about the radius of curvature R for the lens, we cannot determine the exact value of R2 or the focal length fn2. However, we know that R2 will be positive (since it is the radius of curvature for the convex side of the lens) and 1.8 times the value of R.