Question

find the radii of curvature of convex concave convergent lens made of glass with refractive index n is equal to 1.5 having focal length of 24 cm and radii of curvature is double the other​

Answer 1

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

Answer 2

$\rm\large{\underline{\underline\color{green}{Given:-}}}$

• N = 1.5 .

• f = 24

$\rm\large{\underline{\underline\color{green}{find:-}}}$

• find the radii of curvature of convex concave convergent lens made of glass with refractive index .

$\rm\large{\underline{\underline\color{green}{Solution:-}}}$

We have,

$\rm \dashrightarrow\frac{1}{f} = (n - 1) ({ \frac{1}{r} - \frac{1}{2r} })$

$\rm \: \dashrightarrow \frac{1}{24} = (1.5 - 1)( \frac{1}{r} - \frac{1}{2r} )$

$\rm\dashrightarrow \frac{1}{24} = 0.5 \times \frac{1}{2r}$

$\rm\dashrightarrow 2r = 0.5 \times 24$

$\rm\dashrightarrow {r = \frac{0.5 \times 24}{2} = 6cm}$

$\longmapsto\sf\boxed {\bold{{ r_{1} = 6cm \: . r_{2} = 12cm.}}}$