Destroying a Building Using a Lens

[ab200]

Homework Statement

I want to mount a giant burning lens on the new engineering building and melt down the student commons. The lens will sit 60 m away from the commons (laterally) and tower 40 m above its roof. I can only afford to grind one side of the giant lens to be spherical, so the other side will have to be flat. The glass will have an index of 1.5. What radius of curvature in m is needed to focus the suns rays onto the commons?

Relevant Equations

(1/s) + (1/s') = 1/f = (n-1)[(1/R1) - (1/R2)]
(n1/s) + (n2/s') = (n2 - n1)/R

Putting the questionable nature of my professor's problem-writing aside, I found this question pretty confusing. I assumed that 60 m was the focal length, and that R1 was infinity since it is a flat surface. This gives me:
1/60 = (1.5 - 1)[(1/∞) - (1/R2)]
This gave me R2 = 30 m, but that isn't correct.

 

[hutchphd]

Homework Statement: I want to mount a giant burning lens on the new engineering building and melt down the student commons. The lens will sit 60 m away from the commons (laterally) and tower 40 m above its roof. I can only afford to grind one side of the giant lens to be spherical, so the other side will have to be flat. The glass will have an index of 1.5. What radius of curvature in m is needed to focus the suns rays onto the commons?
Relevant Equations: (1/s) + (1/s') = 1/f = (n-1)[(1/R1) - (1/R2)]
(n1/s) + (n2/s') = (n2 - n1)/R

Putting the questionable nature of my professor's problem-writing aside, I found this question pretty confusing. I assumed that 60 m was the focal length, and that R1 was infinity since it is a flat surface. This gives me:
1/60 = (1.5 - 1)[(1/∞) - (1/R2)]
This gave me R2 = 30 m, but that isn't correct.

What is distance?

 

[kuruman]

@hutchphd's queston is well worth considering but there is an additional issue with your answer.

1/60 = (1.5 - 1)[(1/∞) - (1/R2)]

In terms of symbols this becomes

1/s=-(n-1)/R

Is this the correct equation for a plano-convex lens? Look it up.

 

[ab200]

What is distance?

I got it! Thanks for the tip.

 

[Nik_2213]

FWIW, I've read of fires started by sunlight focussed onto adjacent, readily flammable material by the curve of a vase or clear bottle, even the dished base of a drinks can. IIRC, the latter, 'merely' thoughtlessly tossed roadside trash, was determined to be the surprising source of a massive 'bush-fire'...

Let's not forget architectural howlers such as the US and UK skyscrapers whose curved glazed facades did their best to 'Death_Star Zap' their neighbourhood until re-fitted with louvred shades...

 

[berkeman]

I've read of fires started by sunlight focussed

Please link to a credible source. You've been here long enough to know that "I've read somewhere" is not a valid source for PF. Thanks.

 

[Nik_2213]

For the curved building...
https://en.wikipedia.org/wiki/20_Fenchurch_Street

For incendiary ornaments...
https://www.dwfire.org.uk/safety/safety-at-home/causes-of-fires/mirrors-and-glass-ornaments/
https://www.sciencefocus.com/planet...hrough-glass-objects-really-cause-house-fires
https://www.cambridge-news.co.uk/news/local-news/firefighter-give-warning-after-glass-27466821

 

[DaveC426913]

This poor MacGregor owner almost had his boat burn to the pavement from a warped mirror in the head*!



* bathroom, for you landlubbers

 

[jbriggs444]

I've been presented with Youtube videos recently featuring the "solar death ray" -- a Fresnel lens salvaged from an old projection TV.

https://www.instructables.com/Solar-Death-Ray-TV-Fresnel-Lens/

Much more fun than burning ants. Hazardous without eye protection and due care though.