L5 - the focimeter

Question 1

what is the thin lens approximation ?

Answer 1

. assuming thickness if lens is small we can treat lens as a single plane with refraction and change of vergence happening at a single plane

Question 2

what are some times of lenses ?

Answer 2

. concave
. convex
. bi-concave
. bi- convex
. plano-concave
. plano-convex
. meniscus

Question 3

what is newton’s equation?

Answer 3

. alternative way of solving object - image problems

. can find image if we know where object is

Question 4

how is newton’s equation derived ?

Answer 4

. we use the theory of similar triangles having same ratio
1. M= h’/h = x’/-f’ = -f/x
2. xx’ = ff’
3. xx’ = ff’
4. for a thin lens f’=-f focal length are same
therefore newton’s final equation is
xx’= -f^2

Question 5

what is x and x’ ?

Answer 5

x = distance from F to object
x' = distance form F' to image

Question 6

what is l and l’ ?

Answer 6

l = distance from lens to object
l' = distance from lens to image

Question 7

what is f and f’ ?

Answer 7

f = distance from lens to F 
f' = distance from lens to F'

Question 8

what is the vertex focimeter ?

Answer 8

instrument that allows us to measure the power of unknown lens could be a spectacle or a contact lens

Question 9

what do we have in a the vertex focimeter ?

Answer 9

. a target which is situated at O
. standard lens ( known power )
. we know where F and F’ are
. positioning stop at F’ opaque screen with hole in the middle

Question 10

how does the vertex focimeter work ?

Answer 10

1. unknown test lens is placed at positioning stop
2. rays coming from object and going through lens will now refract again by test lens
3. light rays leaving test lens can leave in any direction depending on the power of test lens
4. in order for focimeter to work we require a collimated beam at the exit , this means that light rays are parallel to each other or go to infinity
5. vergence coming out of system must be 0
6. to change vergence leaving test lens we need to change vergence arriving at test lens
7. we need to change vergence leaving target and reaching standard lens
8. simplest way is to move target
9. vergence reaching standard lens depends on l and n
10. move target back and forth till we get a collimated beam of light leaving test lens or parallel rays
11. we know we have parallel rays because a target will appear sharp in focus

Question 11

what will happens if we only had a standard lens ?

Answer 11

light rays diverging from object O and and converging to image O’

Question 12

what is the focimeter equation ?

Answer 12

gives power of unknown lens in terms of the power of standard lens squared
Ft = Fs^2 x
x is the position of target as we move target back and forth x will chage depending on power of test lens

Question 13

what happens in a negative test lens ?

Answer 13

in order to get parallel rays emerging O is to the left of first focal point of standard lens
x is negative so Ft is also negative so we have negative power for test lens

Question 14

what happens in a positive lens ?

Answer 14

target must past the first focal point to the right of F
x is still measure of first focal point to target
x is positive as we are measuring from left to right
so we have positive power for test lens

Question 15

what is the significance of focimeter equation ?

Answer 15

it is equation of a straight line
Ft is linearly proportional to x
must move target in a linear fashion in order to get power of test lens