Question

32. An equiconvex lens is made of glass of
refractive index 1.5 and has a focal length
of 10 cm in air. The lens is cut into two equal
halves along a plane perpendicular to its
principal axis to yield two plano-convex
lenses. The two pieces are glued such that
the convex surfaces touch each other. If
this combiantion lens is immersed in water
of refractive index 4/3 its focal length (in
cm) is​

Answer 1

ʟᴇɴ'ꜱ ᴍᴀᴋᴇʀ'ꜱ ꜰᴏʀᴍᴜʟᴀ:-

ꜰ

1

=(μ−1)(

ʀ

1

1

−

ʀ

2

1

)

ꜰᴏʀ ᴇQᴜɪ-ᴄᴏɴᴠᴇx ʟᴇɴꜱ:-

ꜰ

1

=(μ−1)(

ʀ

1

−

−ʀ

1

)

⟹

ꜰ

1

=(μ−1)

ʀ

2

ꜰᴏʀ, ᴛʜᴇ ᴘʟᴀɴᴏ-ᴄᴏɴᴠᴇx ʟᴇɴꜱ ꜰᴏʀᴍᴇᴅ:-

ꜰ

′

1

=(μ−1)(

ʀ

1

1

−

∞

1

)

ꜰ

′

1

=(μ−1)

ʀ

1

⟹ꜰ

′

=2ꜰ

Answer 2

If the combination of lens is immersed in water, its focal length is 40 cm

Explanation:

Given

The focal length of the lens $f' = 10 cm[tex]</p><p>Since this lens is cut into two equal part, the focal length of each part will be</p><p>[tex]=2f'=1\times10=20$ cm

We know that when two lenses of focal length $f_1$ and $f_2$ are kept in contact, then the effective focal length is given by

$\boxed{\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}}$

$\implies \frac{1}{f}=\frac{1}{20}+\frac{1}{20}$

$\implies\frac{1}{f}=\frac{1}{10}$

$\implies f=10$ cm

Therefore, when the two pieces are glued together, there is no change in focal length

Given the refractive index of glass w.r.t. air $_g\mu_a=1.5$

Refractive index of water w.r.t. air $_w\mu_a=\frac{4}{3}$

Refractive index of glass w.r.t. water $_g\mu_w$

$_g\mu_w=\frac{_g\mu_a}{_w\mu_a}$

$\implies _g\mu_w=\frac{1.5}{4/3}$

$\implies _g\mu_w=\frac{4.5}{4}$

if focal length of the lens in water is $f_w$ then

$\boxed{f_w=(\frac{_g\mu_a-1}{_g\mu_w-1})f}$

$\implies f_w=(\frac{1.5-1}{(4.5/4)-1})\times 10$

$\implies f_w=\frac{0.5\times 4}{0.5}\times 10$

$\implies f_w=40$ cm

Hope this answer is helpful.

Know More:

Q: A glass convex lens of refractive index 1.5 has focal length 8 cm when in air what would be focal length of lens when immersed in water of refractive index 1.33.

Click Here: https://brainly.in/question/6531661