Question

Imagine you're in your car, which is equipped with a cortex spherical side mirror. The mirror has a radius of curvature of 25 cm. As you're parked, you notice a car parked 20 m behind you. The car image's height in the mirror is 1.1 cm. Calculate the actual height of the car.

Answer 1

The actual height of the car is 1.21 cm.

Step-by-step explanation:

To calculate the actual height of the car, we can use the magnification formula for spherical mirrors:

Magnification (m) = Image height (hi) / Object height (h0)

Given that the image height in the mirror is 1.1 cm and the radius of curvature is 25 cm, we can rearrange the formula to solve for the object height:

h0 = hi / m

Using the values, we have: h0 = 1.1 cm / m

To calculate the magnification, we need to find the object distance (do) and the image distance (di). Since we're parked and looking at a car parked behind us, the car's image distance will be negative (-20 m) and the object distance will be positive (+25 cm or 0.25 m). The magnification formula is:

m = -di / do

Substituting the values, we have: h1 / h0 = -di / do

Since the magnification is given as 1.1 cm / 1 cm (1.1), we can solve for di:

1.1 = -di / 0.25

Solving for di, we find that the image distance (di) is -0.275 m. Now, substituting this value back into the magnification formula, we can solve for do:

1.1 = (-0.275) / do

Solving for do, we find that the object distance (do) is 0.25 m.

Now, we can calculate the actual height of the car by substituting the object height (h0) and the object distance (do) into the magnification formula:

m = -di / do

Substituting the values, we have: h1 / 1.1 = -0.275 / 0.25

Solving for h1, we find that the actual height of the car is 1.1 cm * (0.275 / 0.25) = 1.21 cm.