Answer:
The lenses with different focal length are four.
Explanation:
Given that,
Radius of curvature R₁= 4
Radius of curvature R₂ = 8
We know ,
Refractive index of glass = 1.6
When, R₁= 4, R₂ = 8
We need to calculate the focal length of the lens
Using formula of focal length
[tex]\dfrac{1}{f}=(n-1)(\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}})[/tex]
Put the value into the formula
[tex]\dfrac{1}{f}=(1.6-1)(\dfrac{1}{4}+\dfrac{1}{8})[/tex]
[tex]\dfrac{1}{f}=\dfrac{9}{40}[/tex]
[tex]f=4.44\ cm[/tex]
When , R₁= -4, R₂ = 8
Put the value into the formula
[tex]\dfrac{1}{f}=(1.6-1)(\dfrac{1}{-4}+\dfrac{1}{8})[/tex]
[tex]\dfrac{1}{f}=-\dfrac{3}{40}[/tex]
[tex]f=-13.33\ cm[/tex]
When , R₁= 4, R₂ = -8
Put the value into the formula
[tex]\dfrac{1}{f}=(1.6-1)(\dfrac{1}{4}-\dfrac{1}{8})[/tex]
[tex]\dfrac{1}{f}=\dfrac{3}{40}[/tex]
[tex]f=13.33\ cm[/tex]
When , R₁= -4, R₂ = -8
Put the value into the formula
[tex]\dfrac{1}{f}=(1.6-1)(\dfrac{1}{-4}-\dfrac{1}{8})[/tex]
[tex]\dfrac{1}{f}=-\dfrac{9}{40}[/tex]
[tex]f=-4.44\ cm[/tex]
Hence, The lenses with different focal length are four.
