1/q + 1/p = 1/f f=r/2 p=15.1
f= 8.55/2= 4.275
1/q= 1/f+1/p= 1/4.275 + 1/15.1 = 19.375/64.5525
take inverse to get q
q= 3.33
f= 8.55/2= 4.275
1/q= 1/f+1/p= 1/4.275 + 1/15.1 = 19.375/64.5525
take inverse to get q
q= 3.33
di= ? h=?
1/do – 1/di = -2/R
1/di = 1/do+2/R = 1/15.1 +2/8.55.
di= 3.33 cm
The virtual image is smaller and closer to the mirror than the object
h/di =H/do =>
h=H•di/do = 6.7•3.33/15.1 =1.48 cm
1/f = 1/dâ‚€ + 1/dáµ¢
where:
f is the focal length of the convex mirror,
dâ‚€ is the object distance (distance of the object from the mirror), and
dáµ¢ is the image distance (distance of the image from the mirror).
In this case, the radius of curvature (R) is given, and for a convex mirror, the focal length (f) is half the radius of curvature:
f = R/2
Substituting the values:
R = 8.55 cm
f = 8.55 cm / 2 = 4.275 cm
Given:
hâ‚€ (object height) = 6.70 cm
dâ‚€ (object distance) = -15.1 cm (negative value since the object is in front of the mirror)
To find the image distance (dáµ¢), we can rearrange the mirror equation:
1/dáµ¢ = 1/f - 1/dâ‚€
Substituting the given values:
1/dáµ¢ = 1/4.275 - 1/(-15.1)
Simplifying the equation:
1/dáµ¢ = 0.2337 + 0.06622
1/dáµ¢ = 0.29992
Taking the reciprocal of both sides:
dáµ¢ = 1/0.29992
dáµ¢ = 3.334 cm
Since the image distance (dáµ¢) is positive, the image is formed on the same side as the object. Therefore, the image is formed 3.334 cm from the convex mirror.
1/f = 1/dâ‚€ + 1/dáµ¢
Where:
f = focal length of the mirror
dâ‚€ = object distance (distance of the object from the mirror)
dáµ¢ = image distance (distance of the image from the mirror)
In this case, we are given:
dâ‚€ = -15.1 cm (negative because the object is placed in front of the mirror)
f = R/2 = 8.55 cm / 2 = 4.275 cm (where R is the radius of curvature)
To find the image distance, we need to rearrange the mirror equation:
1/dáµ¢ = 1/f - 1/dâ‚€
Let's substitute the values into the equation:
1/dáµ¢ = 1/4.275 - 1/-15.1
Now, we can calculate the image distance by taking the reciprocal of the sum on the right side of the equation:
1/dáµ¢ = (1/4.275 + 1/15.1)^-1
Calculating this expression will give us:
1/dᵢ ≈ 0.415
Taking the reciprocal once again, we find:
dᵢ ≈ 2.41 cm
Therefore, the image is formed approximately 2.41 cm behind the convex mirror.