Question

Apply the mirror formula if focal length \( f = l \, \text{m} \) and object distance \( u = 15 \, \text{m}.\)

Hint:

The mirror formula is essential for determining the image distance when the object distance and focal length are known.

Answer 1

Step 1: Understanding the mirror formula.
The mirror formula relates the object distance (\( u \)), image distance (\( v \)), and focal length (\( f \)) of a mirror. It is given by: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Rearranging the formula to solve for \( v \): \[ v = \frac{uf}{u - f} \] Step 2: Conclusion.
Thus, the image distance \( v \) can be calculated using the formula \( v = \frac{uf}{u - f} \). If \( f = l \) m and \( u = 15 \) m, we can substitute these values to find \( v \).

Answer 2

Step 1: The mirror formula connects focal length (f), image distance (v), and object distance (u): 1/f = 1/v + 1/u.

Step 2: Rearranging to find v: v = (u × f) ÷ (u − f).

Step 3: Here the object distance is u = 15 m; plug in the given focal length f into this formula.

Step 4: So the image distance is found from v = uf/(u−f), using the given values of u and f.

Answer 3

The mirror formula itself comes from similar triangles set up by the incident and reflected rays at the mirror's pole and centre of curvature, and combining those triangle ratios gives \( \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} \).
Clearing fractions with a common denominator, \( \dfrac{u + v}{uv} = \dfrac{1}{f} \), so \[ v = \frac{uf}{u - f} \] With the object distance \( u = 15 \, \text{m} \), this expression gives the image distance \( v \) once the focal length \( f \) is substituted in.