Question

An object is located 5.0cm from a concave mirror. The focal length is 15.0cm. What is the image distance?

a) 3.8cm
b) 7.5cm
c) -3.8cm
d) -7.5cm

Answer 1

d) -7.5cm

Step-by-step explanation:

Given :

An object is located 5.0cm from a concave mirror. The focal length is 15.0cm.

Object distance (u) = 5.0 cm

Focal length (v) = 15.0 cm

Solution:

Using mirror's equation,

`\: \longrightarrow \: (1)/(v) + (1)/(u) = (1)/(f)`

Plugging the values into mirror's equation

`\: \longrightarrow \: (1)/(v) + (1)/(5) = (1)/(15) \\`

`\: \longrightarrow \: (1)/(v) = (1)/(15) - (1)/(5) \\`

`\: \longrightarrow \: (1)/(v) = (1-3)/(15) \\`

`\: \longrightarrow \: (1)/(v) = ( - 2)/(15) \\`

`\: \longrightarrow \: (1)/(v) = (1)/(-7.5) \\`

`\: \longrightarrow \: v = - 7.5 \:cm`

• Hence, the image distance is - 7.5 cm

Answer 2

In this case, the image distance is approximately -7.5 cm.

Step-by-step explanation:

To find the image distance in this case, we can use the lens formula: 1/f = 1/do + 1/di. In this formula, f is the focal length of the mirror, do is the object distance, and di is the image distance.

Given that the object distance (do) is 5.0 cm and the focal length (f) is 15.0 cm, we can substitute these values into the lens formula:

1/15 = 1/5 + 1/di

Simplifying the equation gives:

1/15 - 1/5 = 1/di

2/30 - 6/30 = 1/di

-4/30 = 1/di

To isolate di, we can take the reciprocal of both sides:

di = -30/4

di ≈ -7.5 cm

Therefore, the image distance is approximately -7.5 cm.