A plano-convex lens of radius 1.0 m is placed on an optically flat glass plate and is
illuminated by an extended monochromatic source. Assume that the point of contact
is perfect. The diameters of the 10th and 5th dark rings in the reflected light are
4.50 × 10−3m and 3.36 × 10−3m. Next, the space between the lens and the glass plate
is filled with a liquid. The diameter of the 5th ring changes to 3.0×10−3m. Calculate
the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the
wavelength of light is 589 nm.
Answers
convex lens of radius 1.0 m is placed on an optically flat glass plate and is illuminated by an
extended monochromatic source. Assume
that the point of contact is perfect. The diameters of the
10th and 5th dark rings in the reflected light are 4.50 × 10−3m and 3.36 × 10−3m. Next, the space
between the lens and the glass plate is filled with a liquid. The diameter of the 5th ring changes
to
3.0×10−3m. Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the
wavelength of light is 589 nm.
Find:
n
dark
-
? n
bright
-
?
Given:
R=1.0 m
r
5
=
1
.
5
×10
−
3
m
λ=589×10
-
9
m
Solution:
For
dark
ring
:
r
5
=
√
kR
λ
n
(1), where k=5
Of (1)
Þ
n
=
kR
λ
r
5
2
(2)
Of (2)
Þ
n=1.3089
For
bright
ring
:
r
5
=
√
(
2k
−
1
)
R
λ
2n
(3), where k=5
Of (3)
Þ
n
=
(
2k
−
1
)
R
λ
2
r
5
2
(4)
Of (4)
Þ
n=1.178
0
Answer:
(i)
1.3089
(ii)
1.178