The diameter of a nickel is 21 mm . How far from your eye must it...

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Physics

The diameter of a nickel is 21 mm .
How far from your eye must it be held so that it has the sameapparent size as the moon? (Use the astronomical data inside theback cover of the textbook.)

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given

Nickel diameter d= 21 mm = 21*10^-3 m

We know that two round or spherical objects have the same angular diameter, even though they are at different distances from the oswerver.

Â Â they have same angular size, that is d/l nickel = D/L moon

Â Â D diameter of moon = 3474*10^3 m, L distance from moon to earth = 3.84*10^8 m
Â Â Â Â Â Â Â d diameter of nickel = 21*10^-3 m, l=?

Â Â Â Â Â D/L = d/lÂ Â Â Â ==>Â Â l = d*L/D ,
Â Â Â Â Â Â Â Â Â Â l= (21*10^-3*3.84*10^8)/3474*10^3
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â l = 2.3212 m

nickel must be held so that it has the same apparent size as the moon is 2.3212 m from eye.

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