SOLUTION: Hi! I'm having some difficulty with the following problem: If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image wil

Question 196582: Hi!
I'm having some difficulty with the following problem:
If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image will be at a distance y from the lens, where F, x, and y are related by the lens equation below. Suppose that a lens has a focal length of 2.1 cm, and that the image of an object is 4 cm closer to the lens than the object itself. How far from the lens is the object?
1/F = 1/x + 1/y
thanks!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since "the image of an object is 4 cm closer to the lens than the object itself", this means that

Start with the given equation.

Plug in and

Multiply EVERY term by the LCD to clear out the fractions.

Cancel out and simplify

Multiply

Distribute

Multiply EVERY term by 10 to make every number a whole number.

Get all terms to the left side.

Combine like terms.

Notice we have a quadratic in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, since (which doesn't make much sense), this means we'll ignore

So the only answer is

=======================================

Answer:

So the object is 7 cm from the lens.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image will be at a distance y from the lens, where F, x, and y are related by the lens equation below. Suppose that a lens has a focal length of 2.1 cm, and that the image of an object is 4 cm closer to the lens than the object itself. How far from the lens is the object?
1/F = 1/x + 1/y
y-4 = distance the image is from the lens
y = distance the object is from the lens
----
1/2.1 = 1/(y-4) + 1/y
Multiply thru by 2.1y(y-4) to get:
y(y-4) = 2.1y + 2.1(y-4)
y^2-4y = 2.1y + 2.1y - 8.4
y^2 - 8.2y + 8.4 = 0
10y^2 - 82y + 84 = 0
(10y-12)(y+7) = 0
y = 1.2 cm (distance the object is from the lens)
========================================================
Cheers,
Stan H.

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