1 ) A slit of width d is illuminated by red light of wavelength 6500 A . The first minimum will fall at angle 30 degree , if d is:-
A ) 1300 * 10^(-10) m , B
) 130 * 10^(-10) m ,
C ) 13000 * 10^(-10) m , D
) None of these ,
Correct
Answer : - C ) 13000 * 10^(-10) m ,
Solution
: -
Given
Data : -
·
θ
= 30 degree ,
·
n
= 1 ,
·
λ
= 6500 A = 65 * 10^(-10) m , { hence , 1 Aº = 10^(-10) m } ,
·
d
= ? ,
Formula
: -
Ø Ø d sinθ = n λ ,
Ø Ø d (sin 30 ) = ( 1 ) * ( 6500 * 10^(-10)) , { hence , sin30 = 1 / 2 } ,
Ø Ø d ( 1 / 2 ) = 6500 * 10^(-10) m ,
Ø Ø d = 13000 * 10^(-10) m , Answer .
2
) A light is incident normally on a grating , which has (250 line / mm) . Find
the wavelength of spectral lines for which deviation in second order is 30 degree ?
A ) 5 * 10^(-5) m , B
) 1 * 10^(-6) m ,
C )
2 * 10^(-7) m , D ) None of these ,
Correct
Answer : - B ) 1 * 10^(-6) m ,
Solution
: -
Given
Data : -
·
θ = 30 ,
·
m = 2 (
for 2nd order ) ,
·
No. of lines = N = 250 line / mm = 250 * 10^3 lines / m = 2.5 * 10^5 lines / m ,
·
λ = ? (
wavelength ) .
Formula
: -
d
sinθ = m λ ………………. Eq. ( 1 )
Ø Grating element = d = 1 / N = 1 / ( 2.5 * 10^5 ) = 4 * 10^(-6) m .
So , put all values in Eq. ( 1 ) ,
§ d sinθ = m λ ,
§ ( 4 * 10^(-6) ) * ( sin 30 ) = ( 2 ) * ( λ ) , { hence , sin 30 = 1 / 2 }
§ ( 4 * 10^(-6) ) * ( 1/ 2 ) = ( 2 ) * (
λ )
,
§ ( 4 * 10^(-6) ) * ( 1 / 4 ) = ( λ ) ,
§ λ = 1 * 10^(-6) m , Answer .
3
) To get more order of spectra using a diffraction grating , the wavelength of
light should be ……………… ,
A )
Increased , B
) Decreased ,
C ) No change , D ) None of these ,
Correct
Answer : - A ) Increased ,
Because we have formula for diffraction
grating is : -
y =
(m l λ) / d ,
{
hence ,
Ø m = first order , 2nd , ……..
Ø l = distance between screen and slits ,
Ø λ = wavelength ,
Ø d = distance between two slits , } .
} .
So , its shows that by increasing the wavelength
of light , will result in increasing the order of spectra .
4
) If no. of lines are halved , then what
would be the effect on grating element of a spectrometer ?
A ) becomes 2 times , B
) becomes quadruple ,
C ) becomes half , D ) None of these ,
Correct
Answer : - A ) becomes 2 times ,
Solution
: -
Formula
: - Grating element = d
= 1 / N ,
Hence , NÍ´ = N / 2 ,
So ,
Ø dʹ = 1 / Nʹ ,
Ø dʹ = 1 / (N/2)
,
Ø dʹ = 2 (
1/ N ) ,
Ø dʹ = 2 * d , Answer .
So
, it will get double .
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