Class 10 > Unit # 13: Geometrical Optics > Image Formation by a Concave Mirror

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Geometrical Optics - Image Formation by Concave Mirrors

Determine position, size, and nature of image formed by a concave mirror.

The position, size, and nature of the image formed by a concave mirror depend heavily on the distance of the object from the mirror. Below are the six standard cases:

(i) Object at Infinity

Rays parallel to the principal axis originating from a distant object converge after reflection to form an image at the principal focus ($F$) in front of the mirror.

• Position of Image: At focus $F$
• Size of Image: Highly diminished (point-sized)
• Nature of Image: Real and inverted

Figure: Ray diagram when object is placed at infinity.

(ii) Object Beyond C

When the object is placed beyond the center of curvature ($C$), the reflected rays meet between focus $F$ and center of curvature $C$.

• Position of Image: Between $F$ and $C$
• Size of Image: Small in size (diminished)
• Nature of Image: Real and inverted

Figure: Ray diagram when object is placed beyond C.

(iii) Object At Center of Curvature ($C$)

When the object is placed directly at the center of curvature, the reflected rays converge right back at the same position.

• Position of Image: At $C$
• Size of Image: Equal in size to the object
• Nature of Image: Real and inverted

Figure: Ray diagram when object is placed at C.

(iv) Object Between $F$ and $C$

When the object is positioned between the focus and the center of curvature, the reflected rays intersect beyond $C$.

• Position of Image: Beyond $C$
• Size of Image: Large in size (magnified)
• Nature of Image: Real and inverted

Figure: Ray diagram when object is placed between F and C.

(v) Object at Focus ($F$)

Taking a ray parallel to the principal axis and another passing through the center of curvature, the reflected rays travel parallel to each other and meet at infinity.

• Position of Image: At infinity
• Size of Image: Highly enlarged
• Nature of Image: Real and inverted

Figure: Ray diagram when object is placed at F.

(vi) Object Between Pole ($P$) and Focus ($F$)

When the object is placed between the pole and focus, the reflected rays diverge and do not meet in front. However, when extended backward, they intersect behind the mirror.

• Position of Image: Behind the mirror
• Size of Image: Large in size (magnified)
• Nature of Image: Virtual and erect

Figure: Ray diagram when object is placed between F and P.