Question

The distance from earth surface to moon surface is 3.8x105 km. Calculate areal spread and angular spread for a laser of wavelength 632.8 nm and aperture 0.5 mm when it reaches moon.

Answer 1

Given:

The distance from the earth surface to the moon surface is 3.8 x 10⁵ km.

To find:

Calculate areal spread and angular spread for a laser of wavelength 632.8 nm and aperture 0.5 mm when it reaches the moon.

Solution:

The wavelength of the laser, λ = 632.8 nm = 6.328 × 10⁻⁷ m

The aperture diameter, d = 0.5 mm = 5 × 10 ⁻⁴ m

The distance from the earth's surface to the moon's surface, D = 3.8 × 10⁵ km = 3.8 × 10⁵ × 10³ m = 3.8 × 10⁸ m

Due to diffraction, the laser beam will spread out after coming out of the aperture. Therefore, the following are the formulas we will use to further solve the problem:

$\boxed{\bold{Angular \:Spread, \:\theta = \frac{1.22 \:\lambda}{d} }}\\\\\boxed{\bold{Areal \:Spread = (D\theta)^2}}$

Finding the angular spread:

The angular spread of the laser beam is,

= θ

= $\frac{1.22 \:\times \: 6.328\times 10^-^7}{5 \times 10^-^4} }}$

= $\boxed{\bold{1.544\times 10^-^3\:radian}}$

Finding the areal spread:

The areal spread of the laser beam is,

= (Dθ)²

= $(3.8 \times 10^8 \times 1.544\times 10^-^3 )^2$

= $(5.8672 \times 10^5 )^2$

= $34.424 \times 10^1^0\:m^2$

= $\boxed{\bold{3.442\times 10^1^1\:m^2}}$

--------------------------------------------------------------------------------------------

Also View:

A laser beam having a wavelength of 8000 Å and aperture of 0.5 cm is sent to the moon. Calculate, (a) Angular spread of the beam (b) A real spread of the beam when it reached the moon. Given the distance of the moon from the earth = 4 x 10 8 m.

brainly.in/question/16597010

A 0.1 watt LASER beam with an aperture of 5.0 mm emits light of wavelength 6943 Å. Calculate the areal spread and intensity of the image when the beam is focused with a lens having a focal length of 100 mm.

brainly.in/question/24906958