Image Formation Lab Worksheet

Study of image formation by convex lens and concave mirror

Objective

To study the nature and size of the image formed by:

A convex lens
A concave mirror

on a screen by using a candle and a screen for different distances of the candle from the lens/mirror.

Materials Required

Optical bench
Convex lens with holder
Concave mirror with holder
Candle/light source with holder
Screen with holder
Measuring scale (meter rule)
Lens cleaning cloth

Theoretical Background

Convex Lens:

A convex lens is a converging lens that converges rays of light passing through it to a point called the focus. The distance between the optical center of the lens and the focus is called the focal length (f).

The lens formula relates the object distance (u), image distance (v), and focal length (f):

\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

The magnification (m) is given by:

\[ m = \frac{\text{Image Height}}{\text{Object Height}} = \frac{h_i}{h_o} = -\frac{v}{u} \]

Cases for Image Formation by Convex Lens:

When object is at infinity: Image is real, inverted, and formed at focus F₂
When object is beyond 2F₁: Image is real, inverted, and formed between F₂ and 2F₂
When object is at 2F₁: Image is real, inverted, same size as object, and formed at 2F₂
When object is between F₁ and 2F₁: Image is real, inverted, magnified, and formed beyond 2F₂
When object is at focus F₁: Image is formed at infinity, real, inverted, and highly magnified
When object is between focus F₁ and optical center O: Image is virtual, erect, magnified, and formed on the same side as the object

Concave Mirror:

A concave mirror is a converging mirror that reflects rays of light to a point called the focus. The distance between the pole of the mirror and the focus is called the focal length (f).

The mirror formula relates the object distance (u), image distance (v), and focal length (f):

\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

The magnification (m) is given by:

\[ m = \frac{\text{Image Height}}{\text{Object Height}} = \frac{h_i}{h_o} = -\frac{v}{u} \]

Cases for Image Formation by Concave Mirror:

When object is at infinity: Image is real, inverted, and formed at focus F
When object is beyond center of curvature C: Image is real, inverted, smaller than object, and formed between F and C
When object is at center of curvature C: Image is real, inverted, same size as object, and formed at C
When object is between F and C: Image is real, inverted, magnified, and formed beyond C
When object is at focus F: Image is formed at infinity, real, and inverted
When object is between pole P and focus F: Image is virtual, erect, magnified, and formed behind the mirror

Experimental Setup

Part A: Convex Lens

Mount the convex lens on the lens holder and place it on the optical bench.
Place the candle (object) on one side of the lens.
Place the screen on the other side of the lens.
Adjust the position of the screen until a sharp image is formed.
Measure the object distance (u) and image distance (v) from the lens.
Repeat the experiment by placing the object at different distances from the lens.

Fig 1: Experimental setup for convex lens

Part B: Concave Mirror

Mount the concave mirror on the mirror holder and place it on the optical bench.
Place the candle (object) in front of the mirror.
Place the screen where the image is expected to form.
Adjust the position of the screen until a sharp image is formed.
Measure the object distance (u) and image distance (v) from the mirror.
Repeat the experiment by placing the object at different distances from the mirror.

Fig 2: Experimental setup for concave mirror

Observations and Calculations

Part A: Convex Lens

Focal length of the convex lens (f) = ________ cm

S.No.	Object Distance (u) cm	Image Distance (v) cm	1/u (cm^-1)	1/v (cm^-1)	1/f = 1/v + 1/u (cm^-1)	f = 1/(1/f) (cm)	Nature of Image	Magnification m = -v/u
1
2
3
4
5

Part B: Concave Mirror

Focal length of the concave mirror (f) = ________ cm

S.No.	Object Distance (u) cm	Image Distance (v) cm	1/u (cm^-1)	1/v (cm^-1)	1/f = 1/v + 1/u (cm^-1)	f = 1/(1/f) (cm)	Nature of Image	Magnification m = -v/u
1
2
3
4
5

Ray Diagrams

Convex Lens Ray Diagrams

Draw ray diagrams for at least three different positions of the object in relation to the convex lens:

Fig 3: Ray diagram when object is beyond 2F

Fig 4: Ray diagram when object is at 2F

Fig 5: Ray diagram when object is between F and 2F

Concave Mirror Ray Diagrams

Draw ray diagrams for at least three different positions of the object in relation to the concave mirror:

Fig 6: Ray diagram when object is beyond C

Fig 7: Ray diagram when object is at C

Fig 8: Ray diagram when object is between F and C

Graphical Analysis

For Convex Lens:

Plot a graph between 1/u and 1/v. The graph should be a straight line with slope = 1 and y-intercept = 1/f.

Fig 9: Graph of 1/v vs 1/u for convex lens

For Concave Mirror:

Plot a graph between 1/u and 1/v. The graph should be a straight line with slope = 1 and y-intercept = 1/f.

Fig 10: Graph of 1/v vs 1/u for concave mirror

Discussion and Analysis

Questions for Analysis:

How does the nature of the image change as the object distance changes from infinity to very close to the lens/mirror?
How does the size of the image change as the object distance changes?
Verify the lens/mirror formula using your experimental data. How close are your calculated values of focal length to the provided value?
What are the possible sources of error in this experiment?
How would you improve this experiment to get more accurate results?

Note on Sign Convention:

For both lens and mirror:

Object distance (u) is positive if the object is on the left side of the lens/mirror (real object).
Image distance (v) is positive if the image is on the right side of the lens/mirror (real image).
Image distance (v) is negative if the image is on the left side of the lens/mirror (virtual image).
Focal length (f) is positive for convex lens and concave mirror.
Focal length (f) is negative for concave lens and convex mirror.

Conclusion

From this experiment, we can conclude:

The image formed by a convex lens or concave mirror depends on the position of the object relative to the focal point and center of curvature.
The lens/mirror formula \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\) is verified by our experimental data.
The magnification formula \(m = -\frac{v}{u}\) is also verified.
The focal length of the lens/mirror can be determined by plotting a graph between 1/u and 1/v.

Focal length calculated from the graph:

For convex lens: f = ________ cm

For concave mirror: f = ________ cm

Important Formulas and Concepts

Key Formulas:

Lens/Mirror Formula: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

Magnification: \[ m = \frac{h_i}{h_o} = -\frac{v}{u} \]

For thin lenses: \[ P = \frac{1}{f} \]

Where P is the power of the lens in diopters when f is in meters.

Summary of Image Formation:

Convex Lens:

Position of Object	Position of Image	Nature of Image	Size Relative to Object
At infinity	At focus F₂	Real and inverted	Highly diminished
Beyond 2F₁	Between F₂ and 2F₂	Real and inverted	Diminished
At 2F₁	At 2F₂	Real and inverted	Same size
Between F₁ and 2F₁	Beyond 2F₂	Real and inverted	Enlarged
At focus F₁	At infinity	Real and inverted	Highly magnified
Between F₁ and optical center O	On the same side as object	Virtual and erect	Enlarged

Concave Mirror:

Position of Object	Position of Image	Nature of Image	Size Relative to Object
At infinity	At focus F	Real and inverted	Highly diminished
Beyond center of curvature C	Between F and C	Real and inverted	Diminished
At center of curvature C	At C	Real and inverted	Same size
Between F and C	Beyond C	Real and inverted	Enlarged
At focus F	At infinity	Real and inverted	Highly magnified
Between pole P and focus F	Behind the mirror	Virtual and erect	Enlarged

Self-Evaluation

Rate your understanding of the following concepts on a scale of 1-5 (1 = poor, 5 = excellent):

Understanding of lens/mirror formula: _______
Ability to predict image characteristics based on object position: _______
Ability to draw accurate ray diagrams: _______
Understanding of sign convention: _______
Overall understanding of image formation by lenses and mirrors: _______