# CALCULUS

posted by Samantha

If you could give an explenation with the answers, that'd be wonderful so I actually know how to solve similar problems in the future. :) Thank you so much!

1. A convex lens with focal length f centimeters will project the image of an object on a point behind the lens. If an object is placed a distance of p centimeters from the lens, then the distance q centimeters of the image from the lens is related to p and f by the lens equation: 1/p + 1/q = 1/f

A. If the focal length of the convex lens is supposed to be 5 cm, and if the image is formed 7 cm from the lens, find the distance, p, from the lens to the object. (It’s not necessary to simplify your answer.)

B. Find an expression that gives q as a function of p, assuming that the focal length is a constant of 5 centimeters.

C. Sketch a graph of q as a function of p (i.e., q(p)), assuming that the focal length is a constant of
5 centimeters. Show any important features of the graph.

D. Find lim p->infinity q(p) and lim p->5+ q(p). What do these limits represent physically? What must happen to the distance of the image and the object?

1. Steve

You have the equation -- just plug in the numbers.

1/p + 1/7 = 1/5
1/p = 1/5 - 1/7
1/p = 2/35
p = 35/2

1/p + 1/q = 1/5
1/q = 1/5 - 1/p
1/q = (p-5)/5p
q = 5p/(p-5)

The above is just algebra I, you know.

any online graphing site can do this. Try wolframalpha.com

limit as p->infinity = 5
limit as p->5 = infinity
parallel rays converge to the focal length (their origin is at infinity)

## Similar Questions

1. ### Physics: Lenses

1) A convex lens with a focal lenght of 4.0cm is placed 20.0cm from a concave lens with a focal lenght of 5.0cm. Find the position of the image when the object is placed 12.0c, in front of the convex lens. 2) A double concave lens …
2. ### Science Important

1. A toy of height 18.4 cm is balanced in front of a converging lens. An inverted, real image of height 33 cm is noticed on the other side of the lens. What is the magnification of the lens?
3. ### calculus

If f is the focal length of a convex lens and an object is placed at a distance p from the lens, then its image will be at a distance q from the lens, where f, p, and q are related by the lens equation 1/f = 1/p + 1/q What is the rate …
4. ### physics

A CONVEX LENS PRODUCES O REAL AND INVERTED IMAGE 2.5 TIMES MAGNIFIED AT A DISTANCE OF 25CM FROM THE LENS.CALCULATE THE FOCAL LENGTH OF THE LENS,
5. ### physics

The convex lens of a copy machine has a focal length of 22.0 cm. A letter to be copied is placed 37.0 cm from the lens. (a) How far from the lens is the copy paper?
6. ### physics

A box is placed 50 cm away from a double convex lens. The image is on the opposite side of the lens, is inverted and 50 cm away from the lens. find: a)the focal length of the lens. b)the height of the image. c) using the focal length …
7. ### physics

Because a concave lens cannot form a real image of a real object, it is difficult to measure its focal length precisely. One method uses a second, convex, lens to produce a virtual object for the concave lens. Under the proper conditions, …
8. ### physics

The convex meniscus lens has a 15cm radius for the convex surface and 20cm for the concave surface. The lens is made of crown glass with refractive index, n=1.52 and is surrounded by air. What is the focal length of the lens.
9. ### physics

A convex lens with a focal length of 20 cm is placed in front of a convex mirror with a focal length of 7.5 cm. A luminous object is placed in front of the convex lens at a distance of 40 cm from it. What is the distance between the …
10. ### calculus

A convex lens of a focal length f can be defined by the lens equation 1/f=1/p + 1/q if an object is a distance p from the lens, then the distance q from the lens to the images. For a particular lens, f=2cm and p is increasing find …

More Similar Questions