Thin Lens Problem: Solving for Object Distance w/ Magnification

[LastXdeth]

Homework Statement

(a) How far from a 50.0-mm-focal-length lens must an object be placed it its image is to be magnified 2.00X and be real?

(b) What if the image is to be virtual and magnified 2.00X?

Homework Equations

Thins Lens Equation: 1/f = 1/d_o + 1/d_i

Magnification Equation: M = h_i/h_o = -d_i/d_o

The Attempt at a Solution

I see that we're only given three pieces of information:

• f=50.0mm
• M=2.00
• The image is real

However, I don't know how to incorporate the magnification equation with the Thins Lens Equation.

 

[PeterO]

Homework Statement

(a) How far from a 50.0-mm-focal-length lens must an object be placed it its image is to be magnified 2.00X and be real?

(b) What if the image is to be virtual and magnified 2.00X?

Homework Equations

Thins Lens Equation: 1/f = 1/d_o + 1/d_i

Magnification Equation: M = h_i/h_o = -d_i/d_o

The Attempt at a Solution

I see that we're only given three pieces of information:

• f=50.0mm
• M=2.00
• The image is real

However, I don't know how to incorporate the magnification equation with the Thins Lens Equation.

Draw a ray trace - the answer is then obvious, and comes VERY quickley.

 

[PeterO]

Homework Statement

(a) How far from a 50.0-mm-focal-length lens must an object be placed it its image is to be magnified 2.00X and be real?

(b) What if the image is to be virtual and magnified 2.00X?

Homework Equations

Thins Lens Equation: 1/f = 1/d_o + 1/d_i

Magnification Equation: M = h_i/h_o = -d_i/d_o

The Attempt at a Solution

I see that we're only given three pieces of information:

• f=50.0mm
• M=2.00
• The image is real

However, I don't know how to incorporate the magnification equation with the Thins Lens Equation.

Have you drawn the ray trace yet?

 

[LastXdeth]

Thanks!

I have answered my own question mathematically.

Since the magnification is 2.00, d_i = (2)(d_o). I just plugged it in the lens equation to find d_o.

 

[PeterO]

Thanks!

I have answered my own question mathematically.

Since the magnification is 2.00, d_i = (2)(d_o). I just plugged it in the lens equation to find d_o.

Did you get both the real image and virtual image answers?

 

[LastXdeth]

Yes, a virtual image would have a d_i = -2(d_o) because the virtual image is upright and in front of the lens.