Write the condition of `n^(th)` order maximum in diffraction.

Explanation

(i) Angular width of central maximum given but `2theta=(2lamda)/(d)impliestheta=(lamda)/(d)" "....(1)`
For first light, `theta_(1)=(lamda_(1))/(d)` and for second light, `theta_(2)=(lamda_(2))/(d)`
`:.(theta_(2))/(theta_(1))=(lamda_(2))/(lamda_(1))" "......(2)`
But `theta_(2)` is 30% less that of `theta_(1)`
That is, `theta_(2)=7-%` of `theta_(1)`
`:.(theta_(2))/(theta_(1))=0.7`
From equation (2), `(lamda_(2))/(lamda_(1))=0.7`
`:.lamda_(2)=0.7xx6000Å=4200Å`
That is, wavelength in a liquid is `4200Å`.
Wavelength in air `lamda_(1)=6000Å`
Wavelength in a liquid `lamda_(2)=4200Å`
(ii) Now refractive index of liquid,
`n=(lamda_(1))/(lamda_(2))`
`=(6000)/(4200)`
`:.n=1.43`