In a darkened room, a burning candle is placed 1.84 m from white wall. a lens is placed between candle and wall at a location that causes a larger, inverted image to form on the wall. when the lens is moved 82.4 cm toward the wall, another image of the candle is formed. how far apart are the two object distances that produce these images? answer in units of m

82.4 cm

Explanation:

The object and screen are kept fixed ie the distance between them is fixed and by displacing lens between them images are formed on the screen . In the first case let u be the object distance and v be the image distance

then ,

u + v = 184 cm

In the second case of image formation , v becomes u and u becomes v only then image formation in the second case is possible.

The difference between two object distance ie(  v - u ) is the distance by which lens is moved so

v - u = 82.4 cm

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft