The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

Optics physics intensity question

Part D
https://isaacphysics.org/questions/light_circ_mirror?board=e976568d-610a-4f8a-99d8-46bf75ff7f05

I’m trying to make the area of the cap/ area of sphere =0.25 but I keep getting equations involving h and x (obviously I’m trying to find x so that’s fine) but I can’t get rid of x. I found the video in the final hint helpful so far but could do with a little extra nudge
Original post by Jsmithx
Part D
https://isaacphysics.org/questions/light_circ_mirror?board=e976568d-610a-4f8a-99d8-46bf75ff7f05
I’m trying to make the area of the cap/ area of sphere =0.25 but I keep getting equations involving h and x (obviously I’m trying to find x so that’s fine) but I can’t get rid of x. I found the video in the final hint helpful so far but could do with a little extra nudge


I am not sure are you seeking help or … Because you said that “I found the video in the final hint helpful so far but could do with a little extra nudge” So you have given yourself the extra nudge or you are asking others to give you the extra nudge.

Next, your explanation is also weird. “I’m trying to make the area of the cap/ area of sphere =0.25 but I keep getting equations involving h and x (obviously I’m trying to find x so that’s fine) but I can’t get rid of x.” You want to find x but at the same time, you want to get rid of x. So what do you really want to do? I have never seen a method in maths that you can get rid of x and then solve for x.
Reply 2
Avatar for Jsmithx
Jsmithx
OP
11
Original post by Eimmanuel
I am not sure are you seeking help or … Because you said that “I found the video in the final hint helpful so far but could do with a little extra nudge” So you have given yourself the extra nudge or you are asking others to give you the extra nudge.

Next, your explanation is also weird. “I’m trying to make the area of the cap/ area of sphere =0.25 but I keep getting equations involving h and x (obviously I’m trying to find x so that’s fine) but I can’t get rid of x.” You want to find x but at the same time, you want to get rid of x. So what do you really want to do? I have never seen a method in maths that you can get rid of x and then solve for x.

I’m looking for a nudge (I’m nearly there but not quite)
The x thing is a typo I’m trying to eliminate h (sorry)
Original post by Jsmithx
I’m looking for a nudge (I’m nearly there but not quite)
The x thing is a typo I’m trying to eliminate h (sorry)


It is again best that you post your working.
Reply 4
Avatar for Jsmithx
Jsmithx
OP
11
2πh(x^2 + 0.3^2)^1/2 (area of cap) divided by 4/3π(x+h)^3 (area of sphere) = 1/4
4h(x^2 + 0.09)^1/2 = 1/3 (x+h)^3
144h^2 (x^2 + 0.09)= (x+h)^6
Original post by Jsmithx
2πh(x^2 + 0.3^2)^1/2 (area of cap) divided by 4/3π(x+h)^3 (area of sphere) = 1/4
4h(x^2 + 0.09)^1/2 = 1/3 (x+h)^3
144h^2 (x^2 + 0.09)= (x+h)^6


4/3π(x+h)^3 is the formula for volume instead of the surface area of a sphere. :smile:
Reply 6
Avatar for Jsmithx
Jsmithx
OP
11
Original post by Eimmanuel
4/3π(x+h)^3 is the formula for volume instead of the surface area of a sphere. :smile:

I think by looking at the last hint R=x+h
2πh(x+h)/2π(x+h)^2 = 1/4
4h=x+h
x=3h which seems reasonable but I still don’t know what h is
Original post by Jsmithx
I think by looking at the last hint R=x+h
2πh(x+h)/2π(x+h)^2 = 1/4
4h=x+h
x=3h which seems reasonable but I still don’t know what h is


The following quote is incorrect.
2πh(x+h)/2π(x+h)^2 = 1/4


2π(x+h)^2 is the surface area of a hemisphere and this leads to an incorrect relationship between x and h (x=3h).

Note that there is a right-angled relationship between R, h and d.
Reply 8
Avatar for Jsmithx
Jsmithx
OP
11
Original post by Eimmanuel
The following quote is incorrect.


2π(x+h)^2 is the surface area of a hemisphere and this leads to an incorrect relationship between x and h (x=3h).

Note that there is a right-angled relationship between R, h and d.

I got it! Thank you

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you