Question

If the focal length of a concave mirror is 18 cm, its radius of curvature will be  
   a. 35cm b. 40cm c. 30cm d. 36cm

The Image formed by a concave mirror when the object is placed between the focus and the centre of curvature of mirror is


a.
Virtual erect and diminished


b.
Real inverted and diminished


c.
Real inverted and magnified


d.
Virtual erect and magnified​

Answer 1

Question 1

If the focal length of a concave mirror is 18 cm, its radius of curvature will be:

a. 35cm

b. 40cm

c. 30cm

d. 36cm ✓

Solution

Focal length(f) = 18cm

Radius of curvature(R) = ?

The formula of focal length is given as:

$\: \: \: \: \: \: \: \: \: \bigstar \: \underline{\boxed{\:f={\sf{ \frac{R}{2} }}}} \: \bigstar$

Substituting known values in the formula we get,

$\implies\sf \:18={\dfrac{R}{2} }$

$\implies\sf{R=18×2}$

$\implies\sf{R=\underline{\boxed{\sf{36 \: cm}}}}$

Therefore, its radius of curvature will be 36cm.

Question 2

The Image formed by a concave mirror when the object is placed between the focus and the centre of curvature of mirror is:

a.Virtual erect and diminished

b.Real inverted and diminished

c.Real inverted and magnified ✓

d.Virtual erect and magnified

Explanation

See above diagram.

When the object is placed between F and C, ray AD after reflection passes through F. The second ray AE, falls on the mirror normally and hence retraces the path after reflection. The two rays intersect at A' after reflection. The image (B'A') is formed beyond C. The image is real, inverted and magnified.

Answer 2

1. (d). '36cm' is the correct answer.

2. (b). 'real inverted and diminished' is the correct answer.

Explanation:

1.Given, focal length(f)of a concave mirror=18cm

∴focal length = $\frac{radius}{2}$

⇒radius=$focal length *2$

⇒r=18X2=36cm

Hence, The radius of the curvature will be 36cm

Therefore, option (d) 36cm is the correct answer. So, The radius of the curvature will be 36cm

2. When the object is placed beyond centre of curvature, an image is formed between the focus and the centre of curvature, it is real inverted and diminished.

Hence, The Image formed by a concave mirror when the object is placed between the focus and the centre of curvature of the mirror is real and diminished.

Therefore, (b). 'real inverted and diminished' is the correct answer.