Radiation on cone

A light of intensity $I$ is incident at an angle $\alpha$ with the vertical on a cone with semivertical angle $\theta<\alpha$ , height $H$ and radius $R$

▪ Supposing that the cone is perflectly reflecting i.e. does not absorb or transmit

▪ Supposing that cone is perfectly absorbing i.e. does not reflect or transmit

Find the radiation force on cone in both cases.

#Mechanics

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

For the 2nd case, I have used projection area. It is semicircle and a semi ellipse,

So we can write area= $\frac {\pi R^{2}}{2}+\frac {\pi RH}{2}$

And then use $IA/c$

Is this approach right?

And I have no idea for the first case

Prince Loomba - 4 years, 7 months ago

for the first case the force will become twice of what u have found in the second case .change in momentum will be 2h/lambda .

And if it was a case where here was reflection and absorbtion .then u calculate the force in each case and multiply it with the coefficient of absorbption and reflection respectively (which would be specified in the question )(also to note that a+r=1 where a and r are the coefficients of absorbtion and reflection respectively )

Zerocool 141 - 4 years, 7 months ago

Exactly twice, are you sure? And I havent really found a proof for other half to be ellipse, can you find?

Prince Loomba - 4 years, 7 months ago

@Prince Loomba – ill try proving it .

Zerocool 141 - 4 years, 7 months ago

@Zerocool 141 – Thanks

Prince Loomba - 4 years, 7 months ago

@Prince Loomba – how did u conclude that it would be an area of ellipse only in the first part ?

Zerocool 141 - 4 years, 7 months ago

@Zerocool 141 – I havent. For second I said its half ellipse half corcle, with no proof

Prince Loomba - 4 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$