Question

3.an object is 2 cm high is placed at a distance of 16 cm from a concave mirror .if the mirror produces 3 cm high inverted image then find the focal length and also image distance.
4. an object is placed in front of a spherical mirror.if the image is formed at 4 cm to the right side of the image.calculate its focal length.is the mirror concave or convex.what is the radius of the curvature.

Answer 1

3. h = +2cm
u = -16cm
h' = -3cm
f = ?
v = ?

magnification = h'/h = -v/u
⇒ -3/2 = -v/(-16)
⇒ -3/2 = v/16
⇒ v = 16 * (-3/2)
⇒ v = -24cm

1/v + 1/u = 1/f
⇒ 1/-24 + 1/-16 = 1/f
⇒ (2+3)/(-48) = 1/f
⇒ 5/(-48) = 1/f
⇒ f = -48/5 cm
⇒ f = -9.6 cm

∴ Image distance is -24 from mirror. Image is real and inverted. Focal length is -48/5cm or -9.6cm

4. u = -18cm
v = +4cm
f = ?
R = ?

1/v + 1/u = 1/f
⇒ 1/4 + 1/-18 = 1/f
⇒ (9-2)/(36) = 1/f
⇒ 7/36 = 1/f
⇒ f = 36/7 cm

R = 2f = 36/7 * 2 = 72/7cm

∴ Focal length is +36/7 cm. Since focal length is positive, it is a convex lens. Radius of curvature is 72/7 cm

Answer 2

3)  h = 2 cm      u = -16 cm
     h' = - 3 cm  inverted.  so it is a real image.
     m = -v/u = h'/h = -3/2        => v = 3 u /2 = - 24 cm

  f = uv /(u+v) = - 9.6 cm

4)
Is the object distance = u = -18 cm

The statement is not clear:  "image is  4 cm to the right of image" ?

case 1)    Object is on the left of mirror.  The image is 4 cm to the right of the Object?
        v = - 14 cm   
        f = uv/(u+v) = - 28*14/32 =  - 49/4 cm    => concave mirror.
          R = 2 f = 24.5 cm

case 2)  Object is on the left of mirror.  The image is 4 cm to the right of the Mirror:
               v = +4 cm    u = -18 cm
           f = uv/(u+v) = 18*4/14  = 36/7 cm      Positive =>  convex mirror.
           R = 2 f = 72/7 cm

case 3)  the object is to the right of mirror..  then image is 4 cm to the right of object.
             u = -18 cm         v = -22 cm
             f = uv/(u+v) = - 18*22/40 cm = 9.9 cm
             so convex mirror...  R =  2 f = 19.8 cm