A slit of width d is illuminated by red light of wavelength 6500 A . The first minimum will fall at angle 30 degree , if a is:- A ) 1300 * 10^(-10) m , B ) 130 * 10^(-10) m , C ) 13000 * 10^(-10) m , D ) None of these ,

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  ,        

ؠؠ  d  (sin 30 )  =  ( 1 ) * ( 6500 * 10^(-10))  ,      { hence ,  sin30 =  1 / 2 } ,

ؠؠ  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 2^nd 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 )

ØGrating 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 , 2^nd  , ……..

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 ,    Nʹ = 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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