A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front

A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front of the mirror. Where will the image be formed?

A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front of the mirror. Where will the image be formed?

Step 1: Identify the given values. The focal length (f) of the concave mirror is 10 cm, but since it's a concave mirror, we use -10 cm. The object distance (u) is 30 cm, and we use -30 cm because we follow the sign convention.
Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
Step 3: Substitute the values into the formula: 1/(-10) = 1/v + 1/(-30).
Step 4: Simplify the equation: -1/10 = 1/v - 1/30.
Step 5: Find a common denominator for the right side. The common denominator for 10 and 30 is 30. Rewrite the equation: -1/10 = 3/(30v) - 1/(30).
Step 6: Combine the fractions on the right side: -1/10 = (3 - 1)/(30v) = 2/(30v).
Step 7: Cross-multiply to solve for v: -1 * 30v = 2 * 10, which gives -30v = 20.
Step 8: Divide both sides by -30 to find v: v = -20/30 = -2/3 cm, which simplifies to v = -15 cm.
Step 9: Interpret the result. The negative sign indicates that the image is formed in front of the mirror, 15 cm away.

Mirror Formula – The relationship between the focal length (f), object distance (u), and image distance (v) in mirror optics, expressed as 1/f = 1/v + 1/u.
Sign Convention – Understanding the sign conventions for concave mirrors, where focal length is negative and object distance is negative when measured in the direction of the incoming light.
Image Formation – Determining the characteristics of the image formed by a concave mirror, including its position, nature (real or virtual), and orientation.