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Thin Lens Equation Calculator

Calculate image properties using the thin lens equation and magnification formulas

Parameters

cmⓘ
cmⓘ
cmⓘ
Show Trail

Controls

xⓘ

Calculated Values

Image Distance:
20.00;cm20.00;cm
Magnification:
−1.00;-1.00;
Image Height:
−5.00;cm-5.00;cm
Lens Power:
0.10;diopters0.10;diopters

Examples

Example 1: Camera Lens

A camera lens with focal length 5 cm forms an image of an object 20 cm away.

  • Image Distance: 6.676.67
  • Magnification: −0.33-0.33
  • Image Height: −1.00-1.00

Example 2: Magnifying Glass

A magnifying glass with focal length 10 cm is used to view an object 5 cm away.

  • Image Distance: −10.00-10.00
  • Magnification: 2.002.00
  • Image Height: 4.004.00

Example 3: Diverging Lens

A diverging lens with focal length -15 cm forms an image of an object 30 cm away.

  • Image Distance: −10.00-10.00
  • Magnification: 0.330.33
  • Image Height: 1.331.33

Visualization

Thin Lens Equation

The thin lens equation is a fundamental formula in geometric optics that relates the object distance, image distance, and focal length of a lens. It is given by: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

Lenses can be either converging (positive focal length) or diverging (negative focal length). Converging lenses focus parallel light rays to a point, while diverging lenses spread light rays apart as if they came from a virtual focus.

The magnification of a lens describes how much larger or smaller the image appears compared to the object. It is calculated as M = -di/do = hi/ho, where hi is the image height and ho is the object height.

When the object is placed beyond the focal point of a converging lens, a real, inverted image is formed. When the object is placed between the focal point and the lens, a virtual, upright image is formed.

The thin lens approximation assumes that the lens thickness is negligible compared to the object and image distances, which is valid for most practical applications in geometric optics.

Key Concepts

  • Focal Length (f): Distance from lens to focal point
  • Object Distance (do): Distance from lens to object
  • Image Distance (di): Distance from lens to image
  • Magnification (M): Ratio of image height to object height
  • Real Image: Formed when light rays actually converge
  • Virtual Image: Formed when light rays appear to diverge
  • Converging Lens: Positive focal length, focuses light
  • Diverging Lens: Negative focal length, spreads light

Real-World Applications

  • Camera lenses and photography
  • Microscopes and telescopes
  • Eyeglasses and contact lenses
  • Projectors and magnifying glasses
  • Optical instruments and imaging systems

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Physics Equations

Thin Lens Equation:
1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
Image Distance:
di=dofdo−fd_i = \frac{d_o f}{d_o - f}
Magnification:
M=−dido=hihoM = -\frac{d_i}{d_o} = \frac{h_i}{h_o}
Image Height:
hi=Mhoh_i = M h_o
Lens Power:
P=1fP = \frac{1}{f}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Calculate Image Distance

First, we calculate the image distance using the thin lens equation:

Equation:

di=dofdo−fd_i = \frac{d_o f}{d_o - f}

Calculation:

di=20.00×10.0020.00−10.00=20.00 cmd_i = \frac{20.00 \times 10.00}{20.00 - 10.00} = 20.00 \text{ cm}

Explanation:

The image distance is calculated using the thin lens equation rearranged to solve for di.

2

Step 2: Calculate Magnification

Next, we calculate the magnification using the image and object distances:

Equation:

M=−didoM = -\frac{d_i}{d_o}

Calculation:

M=−20.0020.00=−1.00M = -\frac{20.00}{20.00} = -1.00

Explanation:

Magnification is negative when the image is inverted and positive when upright.

3

Step 3: Calculate Image Height

The image height is found using the magnification and object height:

Equation:

hi=Mhoh_i = M h_o

Calculation:

hi=−1.00×5.00=−5.00 cmh_i = -1.00 \times 5.00 = -5.00 \text{ cm}

Explanation:

The image height is proportional to the object height with the magnification as the constant of proportionality.

4

Step 4: Determine Image Type

Finally, we determine if the image is real or virtual based on the image distance:

Equation:

Image Type={Realif di>0Virtualif di<0\text{Image Type} = \begin{cases} \text{Real} & \text{if } d_i > 0 \\ \text{Virtual} & \text{if } d_i < 0 \end{cases}

Calculation:

di=20.00 cm⇒Real Imaged_i = 20.00 \text{ cm} \Rightarrow Real \text{ Image}

Explanation:

Positive image distance indicates a real image, while negative indicates a virtual image.

Frequently Asked Questions (FAQ)

What is the difference between a real and virtual image?

A real image is formed when light rays actually converge at a point and can be projected onto a screen. A virtual image is formed when light rays appear to diverge from a point and cannot be projected onto a screen.

When is the magnification positive or negative?

Magnification is positive when the image is upright (same orientation as the object) and negative when the image is inverted (upside down compared to the object).

What happens when the object is placed at the focal point?

When the object is placed exactly at the focal point, the image distance becomes infinite, meaning the light rays emerge parallel and no image is formed.

How does a diverging lens differ from a converging lens?

A diverging lens has a negative focal length and always forms virtual, upright images that are smaller than the object. A converging lens has a positive focal length and can form either real or virtual images depending on object position.

What is lens power and how is it related to focal length?

Lens power is the reciprocal of focal length (P = 1/f) and is measured in diopters. A shorter focal length corresponds to higher power and stronger focusing ability.

Practice MCQs

  1. For a converging lens, when is the image real?
  2. The magnification of a lens is -2. This means the image is:
  3. What happens to the image distance as the object approaches the focal point?
  4. A diverging lens always forms:
  5. If the focal length of a lens is doubled, its power:

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