In spherical mirrors, three primary distances are considered:
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- Introduction
- Stepwise Derivation of the Mirror Formula
Introduction:
- Object Distance (u): The distance of the object from the pole of the mirror.
- Image Distance (v): The distance of the image from the pole of the mirror.
- Focal Length (f): The distance of the principal focus from the pole of the mirror.
These quantities are related by a mathematical expression known as the mirror formula:
`"1"/"v"`+`"1"/"u"`=`"1"/"f"`
Stepwise Derivation of the Mirror Formula:
The derivation of the mirror equation establishes the relationship between the object distance (u), image distance (), and focal length (). In the given setup, the two right-angled triangles A′B′F and MPF are identified as similar triangles.
The triangles B′A′F and PMF are similar because they share common angles. Using the property of similar triangles:
`"B'A'"/"PM"`=`"B'F"/"FP"`
Substituting PM=AB into the equation:
`"B'A'"/"BA"`=`"B'F"/"FP"` .............(i)
∠APB = ∠A'PB
△A'B'P' ∼ △AB'P
`"B'A'"/"BA"` = `"B'P"/"BP"` ............(ii)
By comparing equation (i) and (ii), we get
`"B'F"/"FP"`= `"B'P-FP"/"FP"` = `"B'P"/"BP"`
B'P = -ν (image distance),
FP = -f (focal length),
BP = -u (object distance).
Substituting these values:
`"-ν+f"/"-f"` = `"-ν"/"-u"`
`"ν-f"/"f"` = `"ν"/"u"`
On further solving, we get
`"1"/"v"`+`"1"/"u"`=`"1"/"f"`
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Related QuestionsVIEW ALL [9]
Match the following:
| Column I | Column II | ||
| 1. | A plane mirror | a. | The image is erect & smaller in size than the object. |
| 2. | A concave mirror | b. | The image is erect & of the same size as the object. |
| 3. | A convex | c. | Used by dentists to see an enlarged image of teeth. |
| d. | Can form images of objects spread over a large area. |
