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Optical Instruments & Image Recording

Camera

Step into the virtual camera laboratory. Interact with a DSLR lens cutaway, experiment with pinhole shoebox setups, adjust phone camera autofocus, and view real-time exposure and depth-of-field variations through the viewfinder.

Virtual Camera laboratory ⓘ

Turn focus controls and set aperture to capture a perfectly exposed, sharp photograph.

Simulation active

Camera Telemetry

Out of Focus
Focal Length f
50 mm
Aperture (f-number)
f/4.0
Object / Image Distance
150 cm / 5.2 cm
Exposure Level
Perfect Exposure
Linear Magnification
-0.035 x

Working Principle of a Camera

A camera is an optical instrument that records real, inverted images on light-sensitive sensors or film by focusing light through a convex lens.

  • Convex Lens System: refracts incoming light rays from the subject, converging them to form a real, inverted intermediate image inside the camera body.
  • Aperture (Diaphragm): An adjustable circular opening behind the lens elements that limits light entry. Larger f-numbers reduce the aperture opening, letting in less light but increasing the depth of field.
  • Shutter Curtain: A mechanical gate that controls exposure time by opening for a precise fraction of a second.
  • Digital Sensor: Placed at the focal plane, it converts light energy into electronic signals to record the photograph.

Lens Formula

For a camera lens of focal length f, object distance u, and sensor distance v:

Thin Lens Formula

1/f = 1/v - 1/u

F-Number Ratio

The f-number (or f-stop) represents the relative aperture diameter D compared to the lens focal length f:

Relative Aperture Formula

f-number = f / D

Pinhole Camera Optics

A pinhole box contains no lens. It forms an image by selecting only a narrow beam of light rays from each point of the object. This eliminates blur but projects a dim image due to the tiny opening size.

Step-by-Step Solved Problems

Master thin-lens equations, f-number calculations, and image scaling math.

Example 1 Problem Statement

A camera has a convex lens of focal length 50 mm. If it is focused on a person standing 2.0 m in front of the camera, calculate the distance between the lens and the sensor (image distance) and the magnification of the image.

View Mathematical Solution Steps
  1. Given parameters: focal length f = +50 mm = +5.0 cm, object distance u = -2.0 m = -200 cm.
  2. Apply the lens formula: 1/v - 1/u = 1/f.
  3. Substitute values: 1/v - 1/(-200) = 1/5.0 => 1/v + 1/200 = 1/5.
  4. Solve for 1/v: 1/v = 1/5 - 1/200 = 40/200 - 1/200 = 39/200.
  5. Calculate image distance: v = 200 / 39 ≈ +5.13 cm = 51.3 mm.
  6. Calculate linear magnification: m = v / u = 5.13 / (-200) ≈ -0.0256.
  7. The negative sign shows that the image formed on the sensor is real and inverted.

Final Derived Answer: Image Distance v = 51.3 mm behind the lens, Magnification m = -0.026x.

Example 2 Problem Statement

Calculate the aperture diameter of a 100 mm telephoto lens when the camera is set to an f-number of f/4. What happens to the aperture diameter if the setting is changed to f/8?

View Mathematical Solution Steps
  1. Step 1: Recall the f-number formula: f-number = f / D, where f is focal length and D is aperture diameter.
  2. Step 2: Rearrange to solve for diameter: D = f / f-number.
  3. Step 3: Solve for f/4: D = 100 mm / 4 = 25.0 mm.
  4. Step 4: Solve for f/8: D = 100 mm / 8 = 12.5 mm.
  5. Notice that increasing the f-number reduces the aperture diameter, letting in less light.

Final Derived Answer: Aperture diameter at f/4 = 25.0 mm, and at f/8 = 12.5 mm.

Example 3 Problem Statement

A pinhole camera has a length (box depth) of 15 cm. If it is aimed at a 2.0 m tall tree located 10 m away, calculate the height of the inverted image projected on the tracing paper screen.

View Mathematical Solution Steps
  1. Given parameters: object height ho = 2.0 m = 200 cm, object distance u = 10 m = 1000 cm, screen distance (image distance) v = 15 cm.
  2. Recall magnification formula: m = hi / ho = -v / u.
  3. Solve for image height: hi = ho × (v / u) = 200 cm × (15 / 1000) = 200 × 0.015 = 3.0 cm.
  4. The image height is 3.0 cm and it is inverted.

Final Derived Answer: Projected Image Height hi = 3.0 cm.

Self-Check Questions

Question 1

What is the optical difference between focusing a lens camera and focusing a pinhole camera?

Show Answer & Explanation

A lens camera has a narrow depth of field and must be focused by physically moving the lens closer to or further from the sensor until the refracted rays converge on the sensor plane. A pinhole camera blocks non-axial rays, producing a dim but always in-focus image across all distances, requiring no focus adjustments.

Question 2

Explain how f-number affects exposure and depth of field in photography.

Show Answer & Explanation

A smaller f-number (e.g., f/2.0) corresponds to a larger aperture diameter, letting in more light (brighter exposure) but producing a shallow depth of field (blurry background). A larger f-number (e.g., f/16) narrows the aperture, letting in less light but keeping both near and far objects in sharp focus.

Question 3

What is the role of the shutter curtain in a camera?

Show Answer & Explanation

The shutter curtain acts as a light-proof gate in front of the sensor. When the shutter button is pressed, the curtain opens for a fraction of a second (shutter speed), exposing the sensor to light before closing again.

Question 4

Why does a pinhole camera image become brighter but blurrier if the pinhole size is increased?

Show Answer & Explanation

A larger pinhole allows more light rays from each point of the object to pass through, increasing brightness. However, these rays overlap and spread out on the screen rather than converging to a single point, resulting in a blurry image.

Question 5

How do modern smartphone cameras achieve autofocus without bulky lens tubes?

Show Answer & Explanation

Smartphone cameras use tiny voice coil motors (VCM) to slide microscopic lens elements back and forth over a range of just a few millimeters, driven by contrast-detection or phase-detection autofocus algorithms.

Question 6

Why is the intermediate image formed on a camera sensor inverted?

Show Answer & Explanation

A camera uses a convex lens system. Parallel or diverging rays from the top of the object are refracted downward by the lens, and rays from the bottom of the object are refracted upward, resulting in a real, inverted image on the sensor.