Find the radii of curvature of a convex-concave convergent lens
made of glass with refractive index n=1.5 having focal length of
24 cm. One of the radii of curvature is double the other.
Answers
Answer:
Given: a convexo-concave convergent lens made of pf glass with refractive index, ν=1.5 and focal length, f=24cm. It has one of the radii of curvature is double the other
To find its radii of the curvature
Solution:
According to the given criteria,
R
1
=2R
2
for convexo-concave lens R
1
is positive and R
2
is positive
According to the lens maker formula,
f
1
=(n−1)(
R
1
1
−
R
2
1
)
⟹
24
1
=(1.5−1)(
R
1
1
−
2R
1
1
)
⟹
24×0.5
1
=
2R
1
2−1
⟹R
1
=
2
12
=6cm
∴,R
2
=2R
1
=12cm
Hence the radii of the curvature is 6cm and 12cm
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Explanation:
Given data,
refractive index ( n)= 1.5
focal length (f)=24 cm
It has one of the radii of curvature is double the other
To find its radii of curvature:
According to the given data,
R1=R2
For convexo-concave lens R1 is positive and R2 is positive
According to the Lensmaker Formula ,
1/f=(n-1)(1/R1-1/R2)
1/24=(1.5-1) (1/R1-1/R2)
1/24=(0.5)(1/R1-1/R2)
1/24x0.5= (1/R1-1/R2)
1/24x0.5=2-1/2R1
1/12=1/2R1
By cross multiplying,
2R1=12
R1=6
Therefore, R1 = 6cm ,
R2 = 2R1 = 6x2= 12cm
Hence, the radii of curvature is 6 CM and 12 CM....