Lenses and Autocollimation: Altering Focal Length and the Lensmaker's Equation

[reb659]

Homework Statement

a) In the autocollimation experiment of Sec. 3.5, a thin convex lens is placed 25 cm from a pinhole that acts as a point source of light. A plane mirror placed 20 cm behind the lens reflects the light back through the lens, and the reflected light forms a sharp spot beside the pinhole.
What is the focal length of the lens (in cm)?

b) Consider a symmetrical biconvex lens with r1 = r2 = r
How would you alter the lens if you wanted to make the focal length longer?
Make it flatter (more like a flat slide) or make it rounder (more like a sphere)?

A. 1/f = 0
B. 1/f = 2(n - 1)/r
C. 1/f = 2(1 - n)/r
D. 1/f = (n - 1)/r

Homework Equations

1/o+1/i=1/f

(n-1)(2/r)=1/f

The Attempt at a Solution

a)I used the lensmaker's equation but the answer was wrong. Shouldn't this formula apply?

b) Increasing the focal length would occur if the radius was increased. Since it is a biconvex lens, they will increase if the lens is made to go outward more, such as if it was a sphere instead of flat.

 

[jackbean]

Something tells me that I know you :)

Anyway

for (a) Read page 42, section 3.1.2 in your physics lab book
for (b) use equation 3.2 (see below)

(n-1)(1/r' -1/r'') = 1/f
for a biconvex lens, r'' is negative

hence (n-1)(1/r' - 1/-r'') = 1/f
(n-1)(1/r' + 1/r'') = 1/f
but since r' = r'' = r, substitute and solve and you'll get your answer

 

[thomate1]

This would result in a longer focal length because the light rays would have to travel a longer distance to converge at the focal point.