Question

❤️ɦεℓℓσ ƒɾเεɳ∂ร❤️​


ʟɪɢʜᴛ ʀᴀʏ ᴛʀᴀᴠᴇʟ ғʀᴏᴍ ᴠᴀᴄᴜᴜᴍ ɪɴᴛᴏ ᴀ ɢʟᴀss ᴡʜᴏsᴇ ʀᴇғʀᴀᴄᴛɪᴠᴇ ɪɴᴅᴇx ɪs 1.5 .ɪғ ᴛʜᴇ ᴀɴɢʟᴇ ᴏғ ɪɴᴄɪᴅᴇɴᴄᴇ ɪs 30°, ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴀɴɢʟᴇ ᴏғ ʀᴇғʀᴀᴄᴛɪᴏɴ ɪɴsɪᴅᴇ ᴛʜᴇ ɢʟᴀss


รραɱ αɳรωεɾร ωเℓℓ ɓε ɾερσɾƭε∂ ✌️



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Answer 1

Answer:

$\checkmark$ Given:

⇒ Refractive Index ( μ ) = 1.5

⇒ Angle of Incidence ( i ) = 30°

$\checkmark$ To Find:

⇒ Angle of Refraction ( r )

$\checkmark$ Solution:

We know that,

$\bigstar$ Snell's Law

• The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant

Mathematically,

$\blue{\implies \sf n_1 \times sin \theta_1=n_2 \times sin \theta_2}$

$\green{\implies \sf \dfrac{n_2}{n_1} = \dfrac{sin \theta_1}{sin \theta_2} }$

Where,

$\implies \sf n_1=refractive \ index \ of \ medium \ 1$

$\implies \sf n_2=refractive \ index \ of \ medium \ 2$

$\implies \sf \theta_1=angle \ of \ incidence$

$\implies \sf \theta_2=angle \ of \ refraction$

Note:

$\pink{\sf \implies \dfrac{n_2}{n_1}= \mu}$

So,

$\blue{\boxed{\boxed{\sf \mu = \dfrac{sin \theta_1}{sin \theta_2}}}}$

Here,

$\implies \sf n_1=refractive \ index \ of \ vaccum$

$\implies \sf n_1=1$

$\implies \sf n_2=refractive \ index \ of \ glass$

$\implies \sf n_2=1.5$

Therefore,

$\sf \implies \dfrac{1.5}{1}= \mu$

Hence,

$\pink{\sf \implies \mu = 1.5}$

So,

$\red{\implies \sf \mu = \dfrac{sin \ i}{sin \ r}}$

Given that,

⇒ Angle of Incidence ( i ) = 30°

We Found,

$\sf \implies \mu = 1.5$

→ Substituting the above value in the Formula,

We get,

$\implies \sf 1.5 = \dfrac{sin \ 30 }{sin \ r}$

$\sf \implies sin \ r = \dfrac{sin \ 30 }{1.5}$

We know that,

$\blue{\longrightarrow \sf sin \ 30\, ^0=\dfrac{1}{2}}$

So,

$\sf \implies sin \ r = \dfrac{1/2}{1.5}$

$\sf \implies sin \ r = \dfrac{1}{2 \times 1.5}$

$\sf \implies sin \ r = \dfrac{1}{3}$

$\sf \implies sin \ r = 0.333$

Therefore,

$\sf \implies r = sin ^{-1}(0.333)$

$\purple{\sf \implies r = 19.471}$

$\green{\boxed{\boxed{\sf r = 19.471}}}$

Since,

$\sf sin ^{-1}(0.333) = 19.47120$

Hence,

Angle of Refraction ( r )

⇒ r = 19.47 °

Answer 2

Refractive Index of Glass = μ = 1.5

Angle of Incidence = i = 30°

To Find :- Angle of Refraction

By a relation of Snell's Law.

μ = Sin i/Sin r

1.5 = Sin 30°/ Sin r

3/2 = (1/2)/ Sin r

Sin r = 1/3

r = Sin-¹(1/3)