The sun is 150,000,000 km from earth; its diameter is 1,400,000 km. a student uses a 5.2-cm-diameter lens with f = 10 cm to cast an image of the sun on a piece of paper. where should the paper be placed relative to the lens to get a sharp image?

The paper is placed on the focus of the lens then we get the sharp image.

Explanation:

Given that,

Object distance = 150000000 km

Diameter = 1400000 km

Diameter of lens = 5.2 cm

Focal length = 10 cm

We need to calculate the image distance

Using formula of lens

Here,

Hence, The paper is placed on the focus of the lens then we get the sharp image.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.