Question

Using the data collected for each lens, calculate (10 times) the focal length of each lens. For both lenses, use the lens equation 1/p +1/q = 1/f.

Long focal length lens

Position of lens (cm)	Position of screen (cm)
1	23.8	70.0
2	45.6	70.0
3	23.1	72.0
4	48.6	72.0
5	22.3	75.0
6	52.2	75.0
7	21.9	77.0
8	54.7	77.0
9	21.7	79.0
10	56.9	79.0

Short focal length lens

Position of Lens (cm)	Position of Screen (cm)
11.7	70
58.1	70
11.6	72
60.2	72
11.6	75
63.3	75
11.4	77
65.3	77
11.4	79
67.3	79

Answer 1

So we calculate va;ue of focal length from the lens maker formula as,

trial	position of lens p (cm)	position of screen (cm)	q = position of lens- screen (cm)	1/p	1/q	1/f	focal length f (cm)
1	23.8	70	46.2	0.04201681	0.021645	0.063662	15.708
2	45.6	70	24.4	0.02192982	0.040984	0.062913	15.8948571
3	23.1	72	48.9	0.04329004	0.02045	0.06374	15.68875
4	48.6	72	23.4	0.02057613	0.042735	0.063311	15.795
5	22.3	75	52.7	0.04484305	0.018975	0.063818	15.6694667
6	52.2	75	22.8	0.01915709	0.04386	0.063017	15.8688
7	21.9	77	55.1	0.0456621	0.018149	0.063811	15.6712987
8	54.7	77	22.3	0.01828154	0.044843	0.063125	15.8416883
9	21.7	79	57.3	0.04608295	0.017452	0.063535	15.7393671
10	56.9	79	22.1	0.01757469	0.045249	0.062824	15.9175949

Now for short focal length we calculate

trial	position of lens p (cm)	position of screen (cm)	q = position of lens- screen (cm)	1/p	1/q	1/f	focal length f (cm)
1	11.7	70	58.3	0.08547009	0.017153	0.102623	9.74442857
2	58.1	70	11.9	0.0172117	0.084034	0.101245	9.877
3	11.6	72	60.4	0.0862069	0.016556	0.102763	9.73111111
4	60.2	72	11.8	0.0166113	0.084746	0.101357	9.86611111
5	11.6	75	63.4	0.0862069	0.015773	0.10198	9.80586667
6	63.3	75	11.7	0.01579779	0.08547	0.101268	9.8748
7	11.4	77	65.6	0.0877193	0.015244	0.102963	9.71220779
8	65.3	77	11.7	0.01531394	0.08547	0.100784	9.92220779
9	11.4	79	67.6	0.0877193	0.014793	0.102512	9.75493671
10	67.3	79	11.7	0.01485884	0.08547	0.100329	9.96721519