Respuesta :
Answer:
(A). The angular width is [tex]11.26\times10^{-6}\ rad[/tex].
(B). The linear width is [tex]7.64\times10^{-6}\ m[/tex]
Explanation:
Given that,
Diameter of lens = 130 mm
Focal length = 680 mm
Wavelength = 600 nm
(A). We need to calculate the angular radius of the central maxima
Using formula of the angular radius
[tex]\theta =\dfrac{1.22\lambda}{D}[/tex]
Put the value into the formula
[tex]\theta=\dfrac{1.22\times600\times10^{-9}}{0.13}[/tex]
[tex]\theta=5.63\times10^{-6}\ rad[/tex]
We need to calculate the angular width
Using formula of angular width
[tex]d = 2\theta[/tex]
Put the value into the formula
[tex]d=2\times5.63\times10^{-6}[/tex]
[tex]d=11.26\times10^{-6}\ rad[/tex]
(B). We need to calculate the radius of the central maximum at the focal distance of the lens
Using formula of radius
[tex]R=\dfrac{1.22fd}{D}[/tex]
Put the value into the formula
[tex]R=\dfrac{1.22\times0.68\times600\times10^{-9}}{0.13}[/tex]
[tex]R=0.00000382 =3.82\times10^{-6}\ m[/tex]
We need to calculate the linear width
Using formula of linear width
[tex]d=2R[/tex]
Put the value into the formula
[tex]d=2\times3.82\times10^{-6}[/tex]
[tex]d=0.00000764= 7.64\times10^{-6}\ m[/tex]
Hence, (A). The angular width is [tex]11.26\times10^{-6}\ rad[/tex].
(B). The linear width is [tex]7.64\times10^{-6}\ m[/tex]
