## User: Manan Bothra

Manan Bothra •

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#### Posts by Manan Bothra

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... N = 4000 line/cm, λ = 5000 x10$^{-8}$, n= 3
$
\frac{dθ}{dλ}= \frac{n}{(a+b)cosθ} \\[3ex]
(a+b) sinθ = nλ \\[2ex]
sinθ = \frac{nλ}{(a+b)} \\[2ex]
sinθ = N nλ \,\,\,\,\,\ [\because (a+b) = \frac{1}{N}] \\[2ex]
sinθ = 4000 \times 3 \times 5000 \times 10^{-8} = 0.6 \\[2ex]
θ= 36.86
$
cosθ = ...

written 2 days ago by
Manan Bothra •

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... RP = $\frac{λ}{dλ}$ = nN
For wavelengths 5140.34 & 5140.85 Å……..
Mean wavelength λ is $\frac{5140.34 + 5140.85}{2} = 5140.595 \ A° $
Smallest difference between them is 5140.85 – 5140.34 = 0.51 A°
First order, n=1
$ N= \frac{1}{n} \times \frac{λ}{dλ} = \frac{1}{1} \times \frac{5140.59 ...

written 2 days ago by
Manan Bothra •

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... Width = 0.5 cm, N = 5000 lines /cm
Therefore total number of lines on grating is $\frac{5000}{0.5} = 10000 $
Mean wavelength λ is $\frac{ 5890.2 + 5896.4}{2} = 5893.3 \ A° $
Smallest difference between them is 5896.4 – 5890.2 =6.2 A°
$ RP = \frac{λ}{dλ} = \frac{5893.3}{6.2} = 950.5 $
Als ...

written 2 days ago by
Manan Bothra •

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... N = 10000 lines/cm, Width W = 5 cm, λ = 6000 Å, n = 2, RP = ?, dλ = ?
Total number of lines on grating are N = 10000x 5 = 50000
RP = nN
RP = 2x 50000
RP = 100000
$\frac{λ}{dλ}$ = RP
100000 = $\frac{6000 \times 10^{-8}}{dλ}$
dλ = 0.06 A°
...

written 2 days ago by
Manan Bothra •

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... RP = $\frac{\lambda}{d\lambda}$ = nN
$λ = \frac{5890+5896}{2} = 5893 A° $
dλ = 5896-5890 = 6 A°
$\frac{λ}{dλ}$ = 982
982 = 1 x N
Therefore N=982 lines /cm
For grating of width 2 cm N = 982 x2 = 1964
...

written 2 days ago by
Manan Bothra •

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... Width W = 3 cm, N = 7000 lines/cm, λ = 5000 A°
grating element $ (a+b) = \frac{1}{N} = \frac{1}{7000} $
RP is maximum when n is maximum
N is maximum when sin θ =1
(a+b) sin θ = n λ
$ n_{max} = \frac{1}{Nλ} = \frac{1}{ 7000 \times 5000 \times 10^{-8}} = 2.8 $
n cannot be 3 as s ...

written 2 days ago by
Manan Bothra •

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... $ D_{(n+p)}^2 - D_n^2 = \frac{4pλR}{μ} $
For air film, μ = 1
For 12$^{th}$ and 4$^{th}$ dark rings:
$ D_{12}^2 - D_4^2 = 4 \times 8 \times λ \times R $ ………………………………..(1)
For 20$^{th}$ and 4$^{th}$ dark rings:
$ D_{20}^2 - D_4^2 = 4 \times 16 \times λ \times R $ ……………………………….(2)
Dividing ...

written 2 days ago by
Manan Bothra •

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... RP = $\frac{λ}{dλ}$ = nN
dλ = $\frac{λ}{nN}$
Velocity = frequency x wavelength
C= νλ
$ ν = \frac{c}{λ}$……………………………(1)
Differentiate the equation 1
$ dν = -c \frac{dλ}{λ^2} $………………………………(2)
Substituting equation 1 in equation 2,
$ dν = -c \frac{λ}{nN λ^2} $
Therefore, $ dν = -\ ...

written 2 days ago by
Manan Bothra •

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... (a+b) = $\frac{2.54}{15000}$, wavelength λ$_1$ = 4000 AU
$
(a+b) sinθ = n λ_1 \\[2ex]
sinθ= \frac{n λ_1}{(a+b)} \\[2ex]
θ= sin^{-1} (\frac{n λ_1}{a+b}) \\[2ex]
θ= sin^{-1} (\frac{n \times 4000 \times 10^{-8}}{2.54/15000}) \\[2ex]
θ= 0.236 \times n \\[2ex]
$
Substitute value of n as 1,2,3
An ...

written 2 days ago by
Manan Bothra •

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... λ$_1$= 6000 A° = 6 x 10$^{-5}$ cm, λ$_2$ = 4800 A° = 4.8 x 10$^{-5}$ cm, θ$_1$=θ$_2$ =30°, sinθ$_1$=sinθ$_2$=0.5
$(a+b) sinθ_1 = n_1 λ_1 $ ……………………………………(1)
$(a+b) sinθ_2 = (n_1 +1) λ_2 $ …………………………………(2)
Dividing equation 1 and 2,
$
n_1 λ_1 = (n_1 +1) λ_2 \\[2ex]
n_1 λ_1 = n ...

written 2 days ago by
Manan Bothra •

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